118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No.13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. THE VOLUMES OCCUPIED BY THE SOLUTE ATOMS IN CER- TAIN METALLIC SOLID SOLUTIONS AND THEIR CON- SEQUENT HARDENING EFFECTS. BY A. L. NORBURY, M.Sc., University College, Swansea. (A Pufer read &fore THE FARADAY SOCIETY, Noday, November I 2th, 1923. SIR ROBERT ROBERTSON, K.B.E., F.R.S., PRESIDENT, in the chair.) Received Spfe7nbcr I of&, I 9 2 3. Objecf of Research and Contents. The object of the present research was to determine the densities of certain copper a-solid solution alloys in order to calculate the volumes that the solute atoms were occupying in each case, the ultimate object being to compare the values so obtained with the hardness values of the same alloys-the latter having been determined by the author in a previous research.' In order to obtain accurate values, the effects of annealing temperature and cold-work on the density of copper were first studied.The densities of the copper a-solid solutions were then determined, and the results calculated in a certain manner in order to estimate the '' atomic volumes ?? occupied by the solute atoms in each case. The results obtained were then compared with the hardness values, and a certain relationship was brought out.I t was also found that the solute atoms were not occupying their normal atomic volumes, but that in each case a contraction or expansion had taken place-the amount of contraction or expansion apparently increasing as the ' I chemical affinity I' of the solute for the solvent increased. The paper is divided as follows :- I. Method of Determining Densities. 2. Effect of Annealing Temperature and Cold-Work on the Density 3. Density of Commercial Copper. 4. Densities of Certain Copper a-Solid Solutions. 5. Calculation of '' Mean Atomic Volumes " and Comparison of latter 6. Similar Results calculated from Data of Previous Workers. 7. Suggested Explanation of Hardening Effects of Elements in Solid Solution. 8. Contraction or Expansion of Elements in Solid Solution.9. Summary and Conclusions. of Cathode Copper. with Hardness Data. I. Method of Determining the Densities. Most of the specimens weighed 40 to 5 0 grms. ; they were weighed in air and in distilled water. The surfaces of the specimens were " finished 'I with a fine-cut file, all sharp edges and irregularities where bubbles might 586 yoimz. Inst. Metais, 1923, No. I., Vol. 29, pp. 407-444.SOLUTE ATOMS I N METALLIC SOLID SOLUTIONS 587 tend to lodge being removed. As long as this condition was satisfied, it was not found necessary to emery paper or polish the specimens (t$ section 2). For the weighing in water the specimens were suspended by means of a 0.01 inch diam. platinum wire. I t was found that errors arose from surface-tension effects between the wire and the surface of the water.A compensating " platinum wire-of exactly the same weight and length, and dipping into water to exactly the same depth as the suspending wire- was therefore used on the other arm of the balance. The water in the two vessels was levelled by means of a siphon tube filled with water. In making a weighing in water the final balance was obtained by making the pointer swing to the left and noting its point of rest, then making the pointer swing the same number of divisions to the right and again noting its point of rest, equidistant points of rest from the balance pointer's zero indicating that the correct weights had been applied. Besides eliminating surface-tension effects, this method automatically eliminates calculations correcting for the weights in air and in water of the suspending platinum wire. The densities were calculated from the formula :- m A = -(Qt - A) + X W (where m = weight in air, w = weight of water displaced, Qt = density of water at P, X = density of air at 16" = o*oo121.) TABLE DENSITIES OF CATHODE AND COMYERCIAL COPPER SPECIMENS AS ANNEALED AHD AFTER COLD-HAMMERING.~ Specimen. Annealing Temperature and Time. 950" for 2 hours 850" for 2 hours 99 Y9 750" for 2 hours 9 9 9 9 9 9 $ 9 550" fix 66 hours 550" for 2 hours 99 99 400" for 4 hours 9 9 9 9 goo" for 2 hours 9 9 9 9 9 9 9 9 knsity (Corrected; as Annealed. 8'853 8*918 8918 8.878 - - - 8'897 8-918 8908 8'923 8'924 Reduction in Thickness by Cold-hammering. Per Cent. 75 do 60 85 40 50 95 90 - - - - 66 50 do Densit (Corrected) After &ammering.588 SOLUTE ATOMS IN METALLIC SOLID SOLUTIONS 2.Efeci of Annealing Temperaiurc and Cold- Work on the Dznsiiy of The specimens tested were cut from those used in the previous research (la. tit.). The cathode copper specimens were melted under molten barium chloride (to exclude oxygen), were subsequently cold-hammered (about 50 per cent. reduction in thickness), and were then annealed at the tempera- tures stated in Table I. and Figure I. The densities of the specimens as annealed are given in Table I., and plotted in the left-hand margin of Fig. I. I t is thought that the decrease in density with increase in annealing temperature is due to the expansion of gas contained in minute “blow- holes ” in the specimens, although the specimens were quite sound and free from blow-holes in the ordinary sense-none being visible at roo diameters.Cathode Copper. 2 -+ .n I It 4 ,x a a“ ..- 20 30 40 50 60 70 80 90 Percentage reduction in thickness by cold-hammering. FIG. 1.-Densities of cathode copper specimens as annealed (X) and after cold- hammering (.). The effect of cold-hammering on the densities of the various cathode copper specimens will be seen from Fig. I and Table I. With from o to 50 per cent. reduction in thickness the specimens become denser-due pre- sumably to the closing up of the minute blow-holes. With from 50 per cent. reduction onwards the densities of the specimens are very nearly constant at 8.924. A relationship very similar to that shown in Fig. I is shown by Johnson 1 for copper after various amounts of cold-roZling.In the case of cold-drawing, Alkins,2 Kalbaum and others, have shown that the density decreases. 1 Johnson, Journ. Inst. Metals, No. I, 1920, Vol. 23, p. 474. *Alkins, Journ. Inst. Metals, No. I, 1920, Vol. 23, p. 411.AND CONSEQUENT HARDENING EFFECTS 589 3. Dcnsify of Commrcia 2 Copgcr. In Table I. are also shown the densities of three specimens of commercial copper, from three different manufacturers. I t will be seen that this less pure copper has an appreciably lower density than cathode copper (viz. 8.904 as against 8.924). DENSITIES AND TABLE 11. MEAN ATOMIC VOLUMBS " OF COPPER Q-SOLID SOLUTIONS. Wei ht Per t e n t . Added Element. A1 1.92 A1 3-82 A1 5-84 A1 7-02 Si 0.93 Si 1.71 Si 2.29 Si 2.67 Si 2-71 Si 3-83 Mn 2-40 Mn 7.20 Mn 15-37 Mn 31-08 Ni 4'52 Ni 9-20 Ni 14.93 Zn 4-06 Z n 7-86 Zn 11$6 Zn 15'58 Ag 1'44 Ag 2'75 Ag 4'24 Ag 5'53 Sn 1.00 Sn 2.03 Sn 2-96 Sn 3.88 Sn 5'75 ~- Density (Corrected).As Annealed. 8.617 8.320 8'05 I 7'%P 8-81 L 8.643 8'577 8-574 8.391 8.796 8'564 8.710 8,126 7.810 8'913 8'917 8.824 8.884 8.816 8'776 8.688 8'810 8-887 8 - 8 9 8'837 8-927 8.903 8'884 8'873 8.921 After Hammering 50 Per Cent. Reduction. 8'611 8-3 I I 8'043 7'904 8'799 8*642 8.605 8.589 cracked 8'819 8'574 8.712 - - 8.940 8'945 8.939 8'879 8'850 8.777 8.743 8*928 8'955 8.974 8'974 8'927 8.914 8.926 8'922 8-92 I Atomic Per Cent. Addad Element. 4'39 A1 833 A1 12-71 A1 15*05 Si 2.06 si 3'75 Si 4-80 si 5'79 Si 5-87 Si 8-19 Mn 2-77 Mn 8-25 Mn 1.7'38 Mn 34-39 Ni 4-88 Ni 9-89 Ni 15*@ Zn 3'96 Zn 7-66 Zn 1136 Zn 15'1g Ag 0.85 At3 1-64 Ag 2-55 Ag 3'33 Sn 0.54 Sn 1.10 Sn 1'60 Sn 2.11 Sn 3'16 Mean Atomic Weight.02*00 w 4 9 58'97 58'12 62'88 62.28 61 'go 61-56 61-54 60.78 63'36 62.88 62-14 60.72 63'36 63.1 I 62.82 63-65 63'73 63'80 63'88 63-98 64'35 64'73 65-09 63-91 64-50 64'77 65'38 64-21 '' Mean Atomic Volume.' As Annealed. 7-19 7-28 7'33 7'35 7'14 7-15 7-16 7-18 7'18 7-25 7.20 7'34 7'65 7'78 7-11 7'20 7.1 2 7'17 7-22 7-27 7'35 7'24 7'29 7'38 7'16 7-20 7'24 7-29 7'37 - After Hammering io Per Cent. Reduction. 7-19 7'27 7-33 7'36 7-15 7.15 7-16 7'15 7-17 - 7-18 7'33 - - 7-09 7-36 7'04 7'17 7.22 7 '37 7'31 7*=7 7-18 7.21 7'25 7-16 7-19 7'23 7-27 7'33 4. Densities of Certain Copper a-Solid Sotufions. The experiments already described showed that in order to obtain a correct value for the density of copper, it was necessary to close up any minute blowholes by cold-hammering.With 50 per cent. reduction in thickness and onwards fairly constant density values were obtained. In order to compare the densities of the copper a-solid solutions it was decided to hammer them all 60 per cent. reduction in thickness and to keep the size and shape of the specimens as much the same as possible.590 SOLUTE ATOMS IN METALLIC SOLID SOLUTIONS The alloys were melted under barium chloride, cooled in crucible, cold- hammered to about 50 per cent. reduction, and then annealed at suitable temperatures between 600’ and 950° ; their preparation, etc., is described more fully in the previous paper.’ The results for each alloy, “as annealed ” and “ after hammering 60 per cent.,” were obtained with dzyerent pieces cut from the same specimen.They are shown in Table II.,2 and are plotted in Fig. 2. If the densities of these alloys before and after hammering are compared, it will be seen that in a number of cases there is no difference in density. It seems probable, therefore, that the added elements have eliminated the gas which caused unsoundness in the cathode copper specimens. Judging by the different results obtained for cathode and commercial copper, oxygen must have a relatively large effect on the density, and its presence in small amounts probably accounts for some of the irregularities. ..I P B 8’5 8’4 8’3 S’Z 8’1 7’9 I z 3 4 5 6 7 8 g x o r r 1 2 1 3 ~ 4 1 5 Weight per cent.added clement. FIG. 2.-Densities of copper .-solid solutions. The above sources of error, viz., unsoundness and oxygen, would in each The highest value obtained for case tend to giva too low a density value. each alloy has therefore been taken for plotting in Figs. 2 and 36. 5. CuZcuZation of 4 L Mean Atomic VoZumes,” and Comparz3on ‘with Hardness Data. I n comparing the atomic volumes of the elements one is comparing the volumes occupied by equal numbers of atoms of each element (viz., by one gramme atomic weight). I t was desired to compare the volumes occupied by equal numbers of atoms of the copper a-solid solutions in a similar way, in order to calculate the apparent volumes occupied by the solute atoms in each case. The 1 Loc. cit. The densities obtained for the aluminium-copper and the zinc-copper alloys are very similar to those given by Reader, yourn.Inst. Metals, VoI. XVIII., No. 2,1922, p. 322, and Bamford, Ibid., Vol. XVII., No. I, p. 212.cu. ATOMIC PER CENT ADDED ELEMENT FIG. 3a-Log. a + n hardness values plotted against atomic composition, copper caolid eolutions.592 SOLUTE ATOMS IN METALLIC SOLID SOLUTIONS “ mean atomic volumes ” of the solid solutions were therefore calculated as follows :- In a binary alloy of metals A and B. Mean atomic weight = atomic weight A x per cent, A in alloy + atomic weight B x per cent. B in alloy. “ Mean atomic volume ” = The results calculated in this way are shown in the last two columns of Table 11. The “ mean atomic volumes ” from Table 11. are plotted in Fig.36 against atomic composition. of the same alloys, as deter- mined in the previous research,2 are plotted in Fig. 3a for comparison. I t will be seen that the hardness curves (Fig. 3a) are very similar to the “mean atomic volume” curves (Fig. 36). In fact, if one plots dzyerence between hardness of I atomic per cent. solid solution and that of copper, against difirence between “ mean atomic volume ” of I atomic per cent. solid solution and that of copper (as has been done in Fig. 4), there is a simple relationship. Mean atomic weight density of alloy * The hardness values 7’3 7‘2 7’1 I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Atomic per cent. added element. FIG. 3b.--“ Mean atomic volume ” values plotted against atomic composition, Copper a-solid solutions. There is one exception, however, and that is in the case of the silicon- copper solid solutions.This exception will be referred to again later. 6. SimiZar ResuZts CaZcuZufed from Data of Previous Workers. Goebel’s data for the densities of certain lead a-solid solutions have been calculated as (‘ mean atomic volumes,” and are plotted in this form in Fig. 56 4 for comparison with his hardness results in Fig. 5a. The “ mean atomic volume ” differences are plotted against hardness differences in Fig. 6 in the same manner as the results in Fig. 4. I t will be seen that the relationship is very similar to that in Fig. 4, but again there is one exception-the sodium-lead alloys in this case. 1 From the initial slopes of the curves in Fig. 3a. the following increases in the values of log.a + t l , for I atomic per cent. added element have been estimated :-Zn 0.003, N i o 00 $5, A1 0-012, Si 0.016, Mn 0’025, Ag 0’053, Sn wogg. These values have been used in Fig. 4. 3 L O C . cif. 3Goebe1, Zeitschrift filr Mctallkunde, Vol. 14, Sept.-Dec., 1922. 4 This method of plotting shows the limit of solubility of sodium in lead very clearly (cf. Fig. 56).AND CONSEQUENT HARDENING EFFECTS I 2 3 4 5 6 Difference in size of solute and solvent atoms. FIG. +-Hardening effects plotted against difference in size of solute and' solvent atoms (copper a-solid solutions). ~ ~~ I z 3 4 5 6 7 8 g 1 o 1 1 1 ~ 1 3 1 4 1 5 Atomic per cent. added element. FIG. 5a.-Brine11 hardness numbers plotted against atomic composition. Lead a-solid solutions (Goebel's data). : 18'4 3 18'3 cs) 18'2 -g 18.1 ; 18'0 Y 8 E 17'9 17.8 I 2 3 4 5 6 7 8 9 10 11 1 2 1 3 1 4 1 5 Atomic per cent.added element. FIG. 5b.--" Mean atomic volumes " plotted against atomic composition. Lead a-solid solutions (calculated from Goebel's data), VOL. XIX-T23 5 93594 SOLUTE ATOMS IN METALLIC SOLID SOLUTIONS -No I I I I I I 2 3 4 5 6 I - - . . . Difference in size of solute and solvent atoms. FIG. 6.-Hardening effects plotted against difference in size ot solute and solvent atoms. (Lead a-solid solutions, from Goebel’s data,) I 2 3 4 5 6 7 8 9 Atomic per cent. added element. FIG. 7a.-Ultimate stresses plotted against atomic composition, aluminium (Data from 8th and 10th Alloys Research Reports.) =-solid solutions. In Fig. 76 ‘‘ mean atomic volumes ” calculated from data in the eighth 1 I n Fig.7a the an2 tenth2 Alloys Research Reports have been plotted.3 1 Carpenter and Edwards, PPOC. Itrst. Mech. Eng., 1907, pp. 229 and 242. 1 Rosenhain and Archbutt, Proc. Inst. Mech. Eng., 1912, pp. 356 and 385. 3 The ( 6 mean atomic volumes ” have been plotted with the values of the ordinates decre&ng as they ascend, in Fig. 76, in order to bring out the similarity to Fig. 7a more clearly.AND CONSEQUENT HARDENING EFFECTS 595 ultimate stresses of the same alloys are shown. of results show the same general type of relationship. Here again the two sets 7. Suggested Exjlnnation of Hurdening Efecis of EZenzenfs i72 Solid So Zu fion. In view of the relationship brought out by the foregoing results, it is interesting to recall that a large part of Roberts-Austen’s work was directed at trying to prove a relationship between the atomic volumes of the added elements and their effects on the mechanical properties of pure metals.Many suggestions have since been put forward to explain the increased hardness of solid solutions, the most recent, notably, being those of Jeffries and Archer’z who ‘( have attributed the hardness of solid solutions largely to increased inter-atomic forces” and to interference with slip; and of 99’ 9-92 -6 993 P zl 996 5 997 - 994 *i 995 ld 998 9’99 10’00 X I 2 3 4 5 6 7 8 9 Atomic per cent. added element. FIG. 7b.--“ Mean atomic volumes ” plotted against atomic composition, aluminium a-solid solutions. (Data calculated rrom 8th and 10th Alloys Research Reports.) Rosenhaiq3 who states, “ since the amount of distortion which the intro- duction of a given ‘dissolved’ atom produces in the space-lattice of the solvent metal governs both the limiting solubility of the dissolved metal and the degree of hardening produced in the solvent metal, we should expect to find that the hardening effect of one metal upon another in the form of a solid solution should, to a first approximation be inversely pro- portional to its solid solubility.” Although the above are in general agree- ment with the foregoing results, neither of these theories fully explains them.I t is suggested that two types of solid solution must be assumed: (u) atomic solid solutions, and (b) molecular solid solutions. The ex- It may be assumed that the Brine11 hardness curves of these alloys would be very Jeffries and Archer, Chem.and Met. Eng., Feb. 8th, 1922, p. 249. similar to those shown in Fig. 7a. 3 Rosenhain, Proc. Roy. SOL, Series A, Vol. gg, No. 2698.596 SOLUTE ATOMS IN METALLIC SOLID SOLUTIONS ceptions in Figs. 4 and 6 (viz., Si in Cu and Na in Pb) being of the second type- In the first type, atoms of solute replace atoms of solvent and distort the latter‘s space-lattice 1 according as they differ in size from the solvent atoms. I t will be seen from Fig. 4, however, that this effect is not a simple linear one. Considering the portion of the curve between the intercept and the positions of Zn and Ni,2 the indication seems to be that the space- lattice of copper can suffer a certain amount of distortion before the hard- ness is materially affe~ted.~ Further distortion of the space-lattice (viz., between the position of Zn and Ag, respectively, on the curve) causes an almost linear increase in the hardening effect.With still further distortion (viz., Ag to Sn) the hardening effect tends to approach a maximum. The greater the distortion the greater the hardening effect. Similar remarks apply to the curve shown in Fig. 6 . I t is possible that the “ chemical affinity ” effects discussed in Section 8 are also influencing the results. Certain exceptional cases (uiz., Si in Cu and Na in Pb., cf: Figs. 4 and 6) do not, however, fall in line with the preceding general explanation, and it is therefore suggested that in these cases ‘‘ molecular solid solutions ” are formed.These exceptional elements have lower atomic weights than any of the other solute elements investigated, and the “ chemical affinity ” between solute and solvent atoms is probably particularly ~ t r o n g . ~ I t is therefore suggested that each atom of these elements has pulled one or more of the surrounding solvent atoms out of the latter’s space-lattice, to form a molecule of inter-metallic compound having a new space-lattice. In the above-mentioned cases, however, these molecules are able to exist dispersed singly throughout the solvent’s space-lattice. The relative interference with slip and consequent hardening would be much greater in this type of solid solution. With regard to the complicated nature of the hardness curves shown in Fig. 3a (viz., bending upwards and then tending to reach a maximum), this is probably explained by space-lattice considerations, the resistance to slip increasing more rapidly than the distortion at first, then, after a certain point, new possible planes of slip tending to become available.With regard to the relationship between hardness and solubility suggested by Rosenhain (Zuc. lit.), the hardness results shown in Fig. 3a indicate that the relationship is not such a simple one. Manganese, for instance, which is believed to form continuous solid solutions with copper, has a relatively large hardening effect. Other factors have apparently to be taken into account. They do not, however, cause a new space-lattice to be formed, as Bain (Chem. and Met. Eng., 1922, April 5th, p.655, Abstract) has shown by X-ray analysis in the case of copper containing 30 per cent. zinc, and in the case of certain other solid solutions. 2 Nickel differs from the other solutes plotted in Fig. 4 in SO far as its atoms distort the copper space-lattice by being smaller than the copper atoms. SThis possibility bears some relationship to the fact that small amounts of cold-work do not increase the hardness of copper when the latter is expressed as log. a + n values. 4It will also be seen from Figs. 3b and 5b that the c c mean atomic volume ” curves for these elements are much more curved than those of the others.AND CONSEQUENT HARDENING EFFECT.S Normal Atomic Volume of Solute. 597 Contraction or Expansion. TABLE 111. APPARENT ATOMIC VOLUMES OF SOLUTE ELEMENTS IN CERTAIN DILUTE SOLID SOLUTIONS (Cf.FIG. 8). 7'6 6.6 10.3 9'2 10'0 16'5 11'2 Solute and Solvent. + 1.3 - 0.3 - 0.3 - 1.8 - 3'4 - 3-6 - 0'2 Mn in Copper . . ' . Ni , , , , . . . . Al ,, ,, . . . . Sn ,, ,, . . . . Si ,, , , . . . . ;; :; $ 9 ' - * , , - . . . 22'0 12'8 13'3 16'5 21'2 Na in Lead . . . . Cd ,, ,, . . . . H g ,, ,, . . . . Sn , , , , . . . . Bi ,, ,, . . . . - 3'7 4- 0.9 - 0.5 - 2'2 - 1'2 Zn in Aluminium . . . c u 9, 9 , . . . Apparent Atomic Volume of Solute. I - 8.9 6.3 7'9 8.2 12.8 7'4 10'1 18'3 11.6 14.2 16.0 19.1 9'9 5'2 9 '2 7'1 + 0.7 - 1'9 8. Contraction or Expansion of EZements in SoZid Sobtions. If the initial slopes of the ' L mean atomic volume " curves shown in Figs. gb, gb, 7b are taken, it can be calculated by extrapolation that the solute atoms are (when present in very dilute solid solution) occupying spaces corresponding to the atomic volumes shown in Table III.In this table their normal atomic volumes are also given, also the differences between the two. The question of calculating what expansion or contraction has occurred is difficult owing to the different space-lattices of the elements. For instance, the metal zinc crystallising in a hexagonal space-lattice has an atomic volume of 9.2, and it is calculated that the zinc atoms when present in small quantities in solution in copper and distributed in the more closely packed cen tre-faced-cube lattice of copper have an apparent atomic volume of 8.0. The question would be simpler were it known what volume the zinc atoms would occupy if the metal crystallised in the more closely packed centre-faced-cube lattice as do the copper atoms.The above factor constitutes an unknown variable, but apart from this the results seem to show a certain relationship. The solute elements which have least "chemical affinity" for copper show the smallest amounts of contraction on entering into solution. Those which have greater affinity show a much larger contraction (and in the case of manganese an expansion). The above is shown in Fig. 8, where the differences between the observed and the normal atomic volumes of the solutes are plotted against the positions the solutes occupy, with respect to copper in the Pehodic Table. In a previous paper1 the relative effects of equi-atomic percentages of various elements in solid solution in increasing the electrical resistivity of 1 Norbury, Trans. Faraday SOC., 1921, VoI.XVII., NO. I, p. 251.598 SOLUTE ATOMS IN METALLIC SOLID SOLUTIONS copper were plotted against their positions with respect to copper in the Periodic Table in a similar manner. I t was suggested (hi. tit.) that the results could be explained as being large or small according as the solute element was near to or far from the solvent in the Periodic Table, that is according to the amount of “ chemical affinity ” between the two. I t is thought that something of the same nature is influencing the results shown in Fig. 8, the apparent contraction or expansion of the solute being greater as the chemical affinity is greater. The same sort of result has been arrived at by Bainl from X-ray analysis of certain solid solutions.“It is rather an interesting fact that in the above solid solutions (Zn and Sn in Cu) the lattice is always stretched somewhat less than would be expected from a proportional increase in lattice size computed from atomic volume considerations. This indicates a weak but perfectly definite attraction between unlike atoms. . . . It is also apparent that the tin and copper atoms pack more closely-considering the volume of the tin atom- than do zinc and copper.” He says :- . THE PERIODIC TABLE Group 7 Group8 Group1 GroupZCroupSGraup4 4.0 I Mn Ni CuAg Zn A1 SnSi Na Cd Hg PbSn Bi plotted against their positions in the Periodic Table with respect to the solvent element. 8.-Differences between observed and normal atomic volumes of elements in dilute solid solution 9.Sormnauy and Condusions. I. In density determinations errors due to surface-tension effects be- tween the surface of the water and the suspending wire may be eliminated by the use of a compensating platinum wire. 2. Cold-hammering has the effect of closing up minute blow-holes in copper. Very severe cold-hammering sets up stresses and strains in the metal which probably cause local increases and decreases in density. Otherwise cold-hammering does not affect the density. 3. Commercial copper has a distinctly lower density than cathode copper. 4. For theoretical purposes there are certain advantages in calculating density results as ‘‘ mean atomic volumes.” 5. When an element is distributed in solid solution as single atoms replacing single atoms of the solvent in the space-lattice of the latter, the hardening effect is, in general, proportional to the difference in size of the solute and solvent atoms.The above relationship does not, however, hold in certain exceptional cases (viz., Si in Cu and Na in Pb), which appear to arise when the solute has an exceptionally strong “chemical affinity” for the solvent. In such cases it is suggested that the solute 1 Bain, Chem. atad Met. Elog., Jan. 3rd, 1923, p. 22.AND CONSEQUENT HARDENING EFFECTS 599 exists in solid solution in the form of molecules of an inter-metallic com- pound having a different space-lattice from that of the solvent. The interference with slip and consequent hardening being relatively much greater in this type of solid solution. 6. When an element forms a solid solution with another element, there is a certain contraction or expansion which seems to be large or small according to whether the " chemical affinity " between the elements is large or small. The author wishes to acknowledge his indebtedness to Professor C. A. Edwards, D.Sc., for facilities for carrying out the present work, and for his interest and encouragement. He also expresses his thanks to the Al58-• c 3'7 3'8 3'9 Hardness (as annealed) before hammering. (Brine11 hardness expressed a s Log. a + 12.) FIG. A.-The effect of cold-hammering in increasing the hardness of the copper or-solid solutions. Royal Society for a Government Grant and to the Institute of Metals for permission to reproduce Fig. 3a. APPENDIX. Tk E'ect oJ Cold-hammering in Increasing tAe Wardnesses of the Coppw SoZid Solutions. From the theoretical point of view it was thought interesting to ascertain whether cold-hammering would increase the hardness of each of the solid solutions to the same extent. The solid solutions were therefore reduced first 60 per cent. in thickness and later go per cent. in thickness and their hardnesses measured after each reduction.600 SOLUTE ATOMS IN METALLIC SOLID SOLUTIONS I t was difficult to hammer all specimens to exactly the same amount and this factor makes the results somewhat erratic; they seem, however, to be sufficiently accurate to show that the nickel-copper solid solutions have hardened relatively less than any of the other solid solutions, which appear to have hardened to equal extents. I n Fig. A their original hardnesses (as annealed) are plotted against their hardnesses after hammering 90 per cent. reduction in thickness. The hardness units employed are not the same, but this does not affect the point in question. The 60 per cent. reduction series were more erratic, but they also showed the lesser hardening of the nickel-copper alloys quite clearly. The above is significant when one recalls the fact that the nickel-copper solutions are the only ones which owe their increased hardness to the presence of a solute element having a smaller atomic volume than copper.