I. Rate and Mechanism of the Hydrolysis of the Hydroxylamine Disulfonate Ion. II. The Low Voltage Electrically Exploded Wire Citation Naiditch, Sam (1947) I. Rate and Mechanism of the Hydrolysis of the Hydroxylamine Disulfonate Ion. II. The Low Voltage Electrically Exploded Wire. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/wne4-hb77. https://resolver.caltech.edu/CaltechTHESIS:04282025-185303011 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry and Physics) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Minor Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Yost, Don M. Thesis Committee: Unknown, Unknown Defense Date: 1 January 1947 Record Number: CaltechTHESIS:04282025-185303011 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:04282025-185303011 DOI: 10.7907/wne4-hb77 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17179 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 30 Apr 2025 16:09 Last Modified: 30 Apr 2025 16:35 Thesis Files PDF - Final Version See Usage Policy. 32MB Repository Staff Only: item control page

I. Rate and Mechanism of the Hydrolysis of the Hydroxylamine Disulfonate Ion II 0 The Low Voltage Electrically Exploded Wire Thesis by Sam Naiditch In Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy Cs.lifornia Institute of Technology Pasadena, California 1947 Acknowledgments I wish to thank Professor Don M. Yost, under whom I have carried out the research presented in this thesis, for initiating and stimulating the program. In addition I am indebted to the late Dr. Horace Russell Jr. and to Professor Verner F. H. Schomaker for supervising a boron investigation that is as yet incomplete. many helpful discussions I have had with Professor William Ha~Nard Pickering regarding the electrically exploded wire problem. TABLE OF CONTENTS Summary 1 Part Io Rate and Mechanism of Hydrolysis of Hydroxylamine Disulfonate Ion 2 Preparation of Materials, Experimental Procedure 2 Results of the Rate Experiments 2 The Reaction Mechanism 5 Summary 6 Part II. The Low Voltage Electrically Exploded Wire 7 A. Introduction 7 B. Apparatus and Experimental Procedure 11 1. The Surge Generator 11 2 0 Preparation of the Filaments 11 3 0 The Filament Explosion Unit 12 Co List of Symbols 14 D. Experimental Results 16 1 0 Minimum Energy Explosions a. Experimental Procedure and Precautions 16 16 b. Appearances of Filaments and Glass Slides 17 c. Results 18 (1) Total Energy Input into Filament per Centimeter 20 (2) End Effects (Behavior of Very Short Filaments 22 (3) Times at which Explosions Occur 23 2. Moderate Energy Explosions 24 a. Effects of Varying Gas Pressure 24 b• Effects of Varying Initial Condenser Voltage 27 c. Effects of Varying Filament Length 31 3. Study of Chemical React ions of Ele ctrica.lly Exploded Filaments with a Number of Gases 36 4. Experiments with Indium Filaments 37 5. An Explosion using Gold Leaf E. Summary and Conclusions 38 39 Appendices A. Derivations 42 1. Derivation of Equation (1) 42 2. Current 44 3. Time at which Explosion Occurs 44 4. Effect of Variation of E and F with Filament Length on E(graphical) for Minimum Energy Explosions 45 5. Mean Filament Resistance Hypothesis and Skin Effect Corrections 45 B. Relations between Mean Filament Resistance and Effective Apparatus Resistance for Minim~~ Energy Explosions 47 C. A Possible Source of the Large Mean Deviations in Explosion Times 48 Do Minimum Energy Explosions with Constantan Filaments for a Number of Different Circuit Constants 49 E. Bibliography 50 Propositions 51 Summary SUMMARY r. Tbe rate of bydrolysis of potassium bydroxylamine disulfonate has been measured. This rate may be satisfactorily accounted for by assuming that HON(S03)2H•H20• is the reaction intermediate whose rate of decomposition into tbe final products determines the over-all rate of hydrolysis. II. The study of the low voltage electrically exploded wire was initiated to see if it could be used as a source of metal vapor. The nature of the processes occuring were checked by determining the amount of energy which is dissipated in the filament by the electrical surge and by examining the metal deposit. For minimum energy explosions, the total energy dissipated in the filament per cm varies a little with filament length, but is unaffected by the substitution of helium for air at atmospheric pressure. The avera ge filament temperature when rupture occurs decreases with increasing filament diameter. As yet no metallic deposits have been found which would } indicate that vapor is present during minimum energy explosions 0 For moderate energy explosions in vacua, the energy dissipated in the filament is independent of pressure changes from 50 to 760 mmo 135 mm. A'.: second process occurs from 10-4 to As yet we cannot be sure whether it is a gaseous discharge or whether the filament has vpporized completely. The two processes overlap from 50 to 135 mm. The appearance of the metal deposits in high vacuum indicate that only vapor has been deposited. For moderate energy explosions in• the atmosphere it is found that the energy input into the filament is a simple function of initial condenser voltage and of filament length 0 When copper filaments have been exploded in a number of different gases at low pressures no resulting changes in pressure w,ere found Part I Ra. te and Mechanism of the Hydrolysis of Hydroxylamine Disulfonate Ion [Reprinlcd from the Journal of the A merican C hemica l Society, 63, 2123 (1041).] [CONTRIBUTION FROM THE GATES AND CRELLIN LABORATORIES OF CHEMISTRY, CALIFORNIA INSTITUTE OF TECHNOLOGY, No . 825] The Rate and Mechanism of the Hydrolysis of Hydroxylamine Disulfonate Ion BY SAM NAIDITCH AN D DON M. YOST Neutral or dilute acid solutions of potassium hyclroxylamine disulfonate hydrolyze at a measurable rate at room temperature to give potassium hydroxylamine monosulfonate and potassium bisulfate, the hydrolytic reaction being, in ionic form HON(S0 3)2- + H20 = HONHSOs- + H + + S0,(1) The hyclroxylamine monosulfonate ion is r elatively stable and does not hydrolyze in dilute acid solution except at higher t emperatures. Wagner 1 made a single measurement on the rate of hydrolysis of the clisulfonate and found it to be proportional to the concentrations of HON(SO3)2and H+. The present paper describes the results of a detailed study of the rate and mechanism of this hydrolysis. Preparation of the Materials. Procedure Experimental Potassium hydroxylamine disulfonate was prepa1·ed according to the method described by Rollefson and Oldershaw 2 in which an ice-cold, acetate-buffered solution of potassium nitrite is treated with sulfur dioxide. The moist salt obtained was washed with iee-eold water and used directly, or it was washed repeat edly with absolute alcohol, and, after drying by evaporation, it was placed in a vacuum desiccator over concentrated sulfuric acid or phosphorus pentoxide and kept at about 5 °. The anhydrous salt thu s prepared, K 2HON(S0 3) 2, could be kept for more than a month without decomposition. In the first 35 runs the freshly prepared, moist salt was washed repeatedly with ice-cold water, and then portions of it were dissolved rapidly in a thermostated volumetric flask nearly filled with a mixture of water and a m easured quantity of hydrochloric acid; time was counted from solution of the salt upon shaking after filling the flask to the mark. For the remainder of the measurements the alcohol -washed salt was used, accurately weighed amounts being dissolved in water in a volumetric flask as b efore. For those experiments in which acid was added initially, hydrochloric acid was used. The reaction was followed by determining t he acid concentration of the reaction mixture at measured intervals. ( 1) Wagner, Z. physik. Chem. , 19, 678 (1896). (2) Rollefson and Oldershaw, THIS JO URNAL , 54, 977 (1932). Samples of 25 or 50 ml. were pipetted into an excess of standard sodium hydroxide to stop the reaction, and the excess base was back-titrated with standard hydrochloric acid, using phenolphthalein as an indicator. Consistent results were not obtainable when the back-titration was postponed for more than about fifteen minutes. All solutions used for the rate runs were carbonate-free, and all flasks were flushed free of carbon dioxide before use. The samples withdrawn from the reaction mixtures were pipetted by means of nitrogen under pressure. During the titration of the mechanically stirred samples, carbon dioxide-free air was passed into the flasks used. That the alcohol-washed, anhydrous K 2HON(S03) 2 was pure is shown by the following experiments, in which accurately weighed amounts of the salt were dissolved in pure water and, after several days, the acid formed was determined by the same procedure as that used for the rate determinations. K2HON(SO,)2 taken, g. Final acid eoncn. found, mole/!, Final acid concn .. calcd ., mole/I. Difi., % 0.6076 .5630 0.00453 . 00417 0.00451 .00418 0.4 .2 It is believed that the present preparations of the pure, anhydrous potassium hydroxylamine disulfonate are the first that have been reported. Results of the Rate Experiments At ionic strengths from about 0.01 to 0.4 m the rate of hydrolysis in acid solution at 25° is adequately represented by the rate equation - d(:ZDs - )/dt = k(:ZDs- )(:zH+) = k(a - x)(b + x) (2) where (2::Ds-) is the total concentration of hydroxylamine disulfonate at the time t, and a is its initial concentration in mole/ I.; b is the initial normality of acid, and x is the normality produced by the hydrolysis of the disulfonate during the time t. This equation may be integrated to give b+x a+b log ~ = _ kt + const. 2 303 (3) The specific reaction rate constants, k, were obtained from the slopes of the plots of log (b + x/a - x) against t. Apparently the acids H 3O+, HSO 4 -, HON(SO3) 2H-, and HONHSO3H, when present in appreciable concentrations, are equally -3- rfi1n c, tnin. In Table I are presented the time- concentration data for four typical experiments made at 0.0 r - - - - , - - - , - -- --,--,-----,-----,,-,----, moderate and at low ionic strengths; in two of these runs acid was added init ially. Table II contains the rate constants found at 25.00° for a number of experiments. The significance of the -0.4 constants shown in the last four columns of the table will appear later. In those runs in which no acid was added t o 39 ..:::, '" bO the disulfonate, the intercepts of the curves with .£ -0.8 the ordinate at zero time (see Fig. 1) were larger + than expected; for example, the inter cept for run ti § 37 corresponds to a value of b = 1.06 X 10- 3 u mole/1. whereas, since no acid was added initially, -1.2 b is at most 10- 6 •8 (determined by use of a glass electrode about one minute after a test solution was made up) . This indicates that the catalyt ic effect of water must be considered. This effect - l.6 ._.___...__ _ _.__ __.__ __.__ _--'---' is included in the rate expression 200 0 600 -WO ~1 ~ 50 0 150 100 250 Time, min. Fig. 1.- Curves for t he evaluation of acid rate constants at 25.00°. effective in catalyzing the reaction in this ionic strength range, since, as may be seen in Fig. 1, the curves show no systematic deviation from linearity. - d(ZDs- )/dt = [k'(ZH+) + k~(H20) ] (ZDs) - = [k'(b + x) + k{v ] (a - x) (4) where k!,, is the rate constant for water cat alysis when the activity of water is t aken as unity. This equation is readily integrated to give ¾\ + x] = [a+ b + ¥,] k't + log [ b + a - X 2.303 TABLE I REPRESENTATIVE Tm!E- CONCENT RATIO N DATA FOR RATE !o{ b ::'.;] (5) MEASUR E MENTS AT 25.00 °, Run 37 Run 42 Run 10 Run 39 a = 0 .0473 a= 0.0495 a = 0.00448 a = 0 .00472 mole/1. b = nonea b = 0.00640 b = b = none" N 0.000152 N µ = 0 . 142 µ = 0. 155 k = 0.262 l k = 0 .257 mole- 1 min.- 1 t, min. µ = 0.0136 0 = 0 .0142 k = 0.837 k = 0.844 x X 10 3 , t, x X 10 2, I, x X 10<, I, mole/!. min. mole/ I. min. mole/!. mi n. 11 1.12 24 1.34 38 1.67 58 2.03 81 2.68 100 3.39 122 4 .32 144 5.32 164 6.65 189 8.93 218 12.08 256 16.17 18 42 60 90 148 178 208 1.199 1.595 1.885 2.428 3.440 3.861 4 .618 242 4.912 57 132 181 236 285 324 376 453 532 618 4 . 50 6.06 7. 14 8.52 10.38 11 .22 12 .90 14.40 17 .88 18.60 181 230 272 318 344 458 503 559 603 x X 10', mole/I. 2.04 2.46 2. 70 3.42 3 .78 5.76 6.90 7.32 8.82 " When the value none is given for the initial acid concentration, it m eans that no acid was added initially. The initial acid concentration is, ther efore, only that obtaining in a solu tion of the <lisul fonat e. When it is assumed, as a first approximation, that the effect of the water catalysis is only important initially, then the rate constants of equation (5) may be obtained graphically from the slopes and intercepts at zero t ime of curves such as t hose shown in Fig. 1. This treat ment was applied to the results for those runs in which no acid was added initially, and the values of k:v so obtained are shown in Table IL Because of the approximation involved in the above method for evaluating k!,,, the following second method was also used in some cases. The simplified rate equation _ d(Z~s- ) = k;~(H,O)(ZDs- ) = k:~(a - x) (6) is applicable in the neighborhood of t = 0, providing no acid was added initially. On integration one obtains log (a - x) = -k;~t/2.30 + log a (7) a nd by evaluating the slope of the log (a - x) versus t curve at zero time (when practically a ll of -4- TABLE II REPRESENTATIVE RATE MEASUREMENTS ON THE HYDROLYSic) OF POTASSIUM HYDROXYLAMINE DISULFONATE AT 25.00° Expt. Initial acid concn., mole/1. Initial conco. of K,HON(SO,),, mole/I. Initial ionic strength, k, 1., mole- 1 min.- 1 µ k~v X 10 4• min.- 1 k', 1., mole - 1 k~~r X 10 \ min.- 1 mia. - 1 ks X 10' min.-1 0.127 0.00640 0.386 0.165 7, 8 0.163 3.2 No ne" .288 .202 .0961 1. 2 2.3 .200 9 3.0 .254 None .208 .0846 3 .8 3 .6 .206 14 2 .8 , 22!) .2:'l9 .0104 . 0762 .227 13 2.6 N one .169 .247 .0566 3 .1 2.G .243 15 2.4 .155 .00640 .257 .0495 .253 10 2.3 .142 None .262 .0473 2.8 3.0 37 .258 2.3 None .0789 .318 .0263 1.1 1. 5 29 . 310 1.7 .0230 None .0689 .348 2.0 2.1 . 339 38 1.8 .0573 .0191 None .414 1. 3 1.2 .403 30 1. 9 .00842 None .0253 .651 40 1.1 .626 1.8 1. f .0142 .837 .00472 None 0.92 39 .792 1. 7 .000152 . 0136 .884 .00448 .798 42 1. 5 .000152 .00835 .998 .00273 .926 41 1.5 • When the value none is given for the initial acid concentration, it means that no acid was added initially; the initial acid concentration is therefore only that resulting from a solution of the disulfonate. the hydrolysis is caused by water), values of k~: are found. These compare favorably with the k~, as may be seen in Table IL The average value found for kw was 2.1 X 10- 4 min. - 1 , and it should be practically independent of the ionic strength. The values of k shown in Table II have been corred.ed for the catalytic effect of the water as follows. From equation 5, neglecting the effect of k~/k' in the logarithm term, the experimental slope, S, is [ a + b + ~ ] 2 ~ 0 hence, k' = k k~/(a + b). The values of k' so calculated are also presented in Table IL Bronsted's equation as modified by Guggenheim, 3 namely log k = log ko + z,z.0 . 1 + Bµ 1 + vµ (8) was used to correlate k' withµ forµ <O.l. On using Fig. 2 and estimating k 0 analytically it was found that log k' = 0.167 - 2 ~ 1 + - - 3.4 µ kw = 0.9 X 10- 2 min.- 1 at 55° - 1 -2 :-1~ ~..s ;> + - 3 <]~ <I -4 (9) µ The results of the experiments made at 45 and 55° are more difficult to treat than those at 25° because the hydrolytic reaction HONHSO,- + H,O = HONH,+ + so,- (10) which may be expected to be catalyzed by acid, can no longer be neglected. A typical log x/t'z, x), t curve at these temperatures is shown in Fig. 3. Features of the reaction to be noted are, (1) the high initial rate, caused by water catalysis; (:l) Gug genheim, Phil . Mag., 19, 588 (l93f>). and (2) the upward concavity of the curve at a later time, caused by the hydrolysis of the monosulfonate to hydroxy}amine. Since the concentrations of both the monosulfonate and acid increase with time, the hydrolysis of the former becomes important. The effect of water catalysis was estimated as before; the values obtained for k~~ (see Table III) are probably high and therefore the smallest are considered most acceptable. kw = 2.0 X 10- 3 min.- 1 at 45° - 5 L-_ _...__ _......__ ____._ __ 0 0.2 0.4 20 (1 + 0)'. 0.6 0.8 Fig. 2.- Curve for the determinat ion of Z1Z 2 and B at 25.00°. Since no acid was added initially at 45 and 55 °, the rate equation for the hydrolysis of the monosulfonate may be assumed to be d(2:HON1:l z)/dt = k2 (~HONHSO 3-) (2:ffl- ) = k,(x - y)(x + y) (11) where x is the amount of disulfona te hydrolyzed, TABLE III RESULTS OF RATE MEASUREMENTS ON THE HYDROLYSIS OF POTASSIUM HYDROXYLAMINE DISULFONATE AT 45 AND 55° No acid was added initially in t!hese experiments. Initial kp ionic k, I. mole- 1 l. mole-1 k~v strength, min.- 1 min.- 1 min.- 1 µ Expt. Initial concn. of K,HON(SO,),, mole/!. 50 51 45 52 47 0 .00577 .04496 .00467 .00342 .00321 0.0173 .0149 .0141 .0103 .0097 5.18 5 .66 5.67 6.32 6.33 t = 45° 4.59 4.25 5.72 6.22 6.41 54 .00457 .00423 .00326 . 01,37 .0127 .0098 14.5 14.8 16.2 t = 55° 14.0 17.7 16.0 55 53 and y is the amount of hydroxylamine formed, in mole/1. On using this equation in conjunction with (2) there results for x < a d(zH+)/dt = kp(ZH+) [a - (1 - P)(zH+)] which integrates to akp [a - (iz~J) (ZH)] = 2 _303 t + const. (12) log where P = kdk. min. - 1 k' 1. molc- 1 min . - 1 1. mole- 1 miu.- 1 3.2 X 10- s 4.7 1.8 3.1 2.2 4.5 X 10- 3 8.3 4.5 4.0 2.7 4.83 5.26 5.24 5.74 5.71 5.29 5.64 5.79 1.9 X 10-2 3.4 3.5 2.1 X 10-2 1. 5 0.91 12.5 12.7 13.4 k:. k~ 12.0 13.2 approximate values of kp. The values of the acid rate constant kp obtained using P = 0.10 are tabulated in Table III. The water catalysis corrections to the rate constants were made as before. The Arrhenius equations for the acid and water catalyzed hydrolysis of hydroxylamine disulfonate were derived for solutions of zero ionic strength and are shown in Table IV which also contains the limiting values of k' and kw. 0.8 TABLE IV THE LIMITING VALUES OF k' AND kw FOR SOLUTIONS OF .,.-._ le:: ZERO IONIC STRENGTH 0.4 I ~ .--( ~ 0.0 .....__,,t:l ..s -0.4 + Temp., °C . k; I. mole-1 min. -1 k~. min.- 1 25.00 45.00 55.00 1.47 10.4 22.0 2.1 X 10-• 2.0 X 10-s 0.9 X 10- 2 k~ = 101,.1 e-17,600/RT I. moie- 1 min.- 1 ot) k~, = 10 13 e-23,000/RT min.- 1 -"' t:: 0 u Time, min. Fig. 3.-Curves showing the effect of the hydrolysis of hydroxylmonosulfonate ion: P = 0, e; P = 0.1, 0 . The Reaction Mechanism The simplest mechanism suggested by the results for the hydrolysis catalyzed by acid assumes that the ion HON(SOa) 2H- forms a reactive complex with water. The over-all rate is determined by the rate at which the complex is converted into the hydrolytic products. It is evident that the concentration of HON(SOa)2H will be determined by that of H +. H+ + HON(S0,)2- ~ HON(S0,)2HThe value of P is not known, but the assumpHON(S03 ).H- + H,O ~ HON(S03) 2H 30tion that an upper limit is P = 0.1 leads, except HON(S0 3) 2H 30 - ---+ HONHS0 3H + HSO,for the initial period in which water catalysis • The rate equation for the hydrolysis will be is important, to the straight line shown in Fig. 3. Since P = 0.10 is probably too large, and since - d(~HON(S0,)2- )/dt = ka(H,O)(HON(S0,)2H-) (13) the P's are different for different ionic strengths, the resulting curves, although more nearly linear and this may be integrated readily on the asthan those obtained previously, will yield only sumption that the ionization constants of the -6- acids HSO4-, HONHSO3H and HON(SO3)2Hare all equal. After lumping several very insensitive terms (terms which vary little with time) into the integration constant, the following integral is obtained for equation (13) for the cases in which no acid was added initially x log a _ x + Clog (a - x) = 2 _303 kBa (a + K) t + const. (14) where K is the acid ioni zation constant for HSO 4-, HON(SO3)2H - and HONHSO3H; C is a constant, less than unity in most cases, and affects the linearity of the log x/a - x, t curves only slightly. Equation (14) differs little from equation (3), and it is for this reason that straight lines were obtained in Fig. 1. As a first approximation k 8 (a + b)/(a - b + K) = k'(a + b) (15) and therefore, kB = k'(a, + K) for those runs in which no acid was added initially. In order to obtain values of kB which may be subjected to inspection, the values of K for HSO 4 - calculated by Pedersen 4 were used, those for the other acids not being known. The values obtained for kB are tabulated in the last column of Table II; for zero ionic strength kB = 1.5 X 10- 2 min. - 1 at 25°, and should be nearly independent ofµ. Whenµ < 0.1, kB is effectively constant as may be seen in the table. (4) Pedersen, J. Phys. Chem., 38, 601 (1934). That the mechanism assumed provides a satisfactory explanation for the experimental results is shown by their accord with the experimentally found rate equation and by the fact that the rate constant kB varies but little with the ionic strength. Summary Anhydrous potassium hydroxylamine disulfonate, K2HON(SQ3)2, has been prepared and kept more than a month without appreciable decomposition. The rate of the hydrolysis HON(S0 3),~ + H20 = HONHSO,- + H+so,- has been measured. For acid solutions the rate equation was found to be -d(1:HON(S0 3),- )/dt = k(1:H +) (1:HON(S0 3),- ) where the sigmas refer to the total concentration of all ions containing the group indicated. Water also catalyzes the hydrolysis, but its effect is much less than that of acid. The effect of temperature on k corresponds to an energy of activation of 17,600 cal. / mole. A mechanism which explains the observations satisfactorily assumes that HON(SO3)2H·H2Ois the intermediate whose rate of decomposition into the final products determines the over-all rate of the hydrolysis. PASADENA, CALIFORNIA RECEIVED MAY 2, 1941 Part II The Low Voltage Electrically Exploded Wire Ao Introduction Several high temperature phenomena have been studied by the electrically exploded -«ir•e method, which consists in discharging a large condenser through a fine metallic filament. Anderson 1 pointed out that the rate of energy input into a filament may be made very large by use of electrical conductivity and Joule beat dissipation, The rate of heat dissipation in his experiments was about 10 9 joules per gram per second. Temperatures abo~e 9,ooo°K and pr~ssures of the order of 30 atmospheres are attained mome ntarily when large energies a.re used 1 , 2 Anderson also demonstrated the absence of 0 several heat loss effects. Anderson and Smith 3 state that after an explosion the vapor first occupies a volume not much larger than the filament and is at high temperature and pressure, then expands with diminishing speed. After 2,0 or 30 microseconds its volume becomes nearly constant at the· pressure of the surrounding atmosphere, its diameter being 2 to 3 cm. Smith 4 found that the mass of the exploding filament had little effect on the maximum voltage across the- vapor. The maximum voltages below were obtained with a o.6 microfarad condenser initially charged to 55 kilovolts for 5 centimeter lengths of filaments. Metal Ag Cu Ni Fe w Zn Al Pb Sn Li Maximum Potentials Across Explosion, kilovolts 81 79 72 39 58 58 51 49 51 42 1. Anderson: Astrophysical Journal, _, 51, 37 (1920). - 2. Futagami: Inst. Phys. Chem. Res. Tokio Sci. Papers, 31, 1 {1937) 0 3o Anderson and Smith: Astrcphysical Journal, 64, 295 {1926). 4. Smith: Ibid, 61, 186 {1925) 0 """" . d Smith 3 Using a rotating•mirror spectrograp, b Anderson an found that throughout ~be first 6 microseconds the spectrum of the explosion is continuous. After about 10 microseconds the continuous spectrum weakens rapidly and is replaced by a spectrum of bright lines similar to that of an arc. The spectrum of an iron wire exploded in a confined volume and photographed end-on by Anderson 1 gave the fallowing results: Pressure, mm Wave length range, .R Spectral characteristics 20 3600-4200 Emission spectrum 50.. 130 " Continuous background increasing in intensity. Reversal becoming prominent. 150-200 760 It Continuous background. Only absorption lines obt~ined. Continuous background. Only absorption lines obtained. Nagaoka and Futagami 5 studied incomplete (low energy) explosions. 2250-5700 'I'bey found that locally the density of luminosity fluctuated greatly. In the case of an incomplete explosion of an aluminum ribbon, the positive end appeared to explode immediately, followed by a minor explosion in the center region, finally by a still smaller explosion at the negative end. Portions of the ribbon apparently did not explode 0 A few effects which depend on the nature of the filament have been found. Anderson 1 stated that it is not possible (with the condenser and voltages be used) to obtain good effects with wires larger than 5 mils or longer than 8 cm 0 Anderson and Smith 3 found that parallel spark gaps discharged the current when vapo~ization bad been completed for all metaB except 5o Nagaoka and Futagami:Pbys Chem. Res. Tokio Sci. Papers,.,§, 269 (1928) Nagaoka and Futagami: Imp. ~cad o Tokio Proc., _g, 387 (1926) Nagaoka, Futagami, and Machida: Ibid, _g, 328 (1926) tungsten. The behavior of tungsten was ascribed to the ionization of the vapor of tungsten at its high boiling point. Anders on 6 found that II copper, silver, and gold a.re anomalous in that the pure wires of these metals will not explode properly when placed in a slot in a block of wood, the main discharge always seeking a path around the outside of the wooden block. By very slightly ,amalgamating the surface of the wires they explode normally, giving fine continuous spectra crossed by their own absorption lines, the lines due to Hg not having been obtained." He also found that "iron vapor as here used is perfectly opaque •• o the absorption coefficient bas been ·shown to be fairly large but has not been measured." Sawyer and Becker? conclude that "the ionization produced in the exploded (aqueous) solution compares w 1th that in the sun and stars of class B" o Similarly, Anderson 1 found that "it requires 200 times the exposure to the sun to produce the same (photographic) density as that given by the explosions". A variety of other studies have been carried out by exploding both metals and aqueous solutions of salts. References to these stuuies will be found in Appendix E. 60 - Anderson: Proc. Nat. Acad. of Sci., 8, 231 (1922) - 7o Sawyer and Becker: Astrophysical Journal, 57, 98 (1923) -10- The rapid heat input of the exploded wire method enables one to investigate metals at high temperatures in an atmosphere at room temperature,. Our original aim was to use the exploded wire as a source of metallic vapor. After attempting to study reactions of exploded copper filaments with a number of gases, we concluded the low voltage explosions were not behaving as anticipated, it being obvious that the filaments were only partially exploded. The voltages we used, 50 to 350 volts, were easier to handle with inexpensive equipment than voltages from 20,000 to 70,000 as used in much of the spectral studies. We studied the effects of the various variabls involved to see how much of the condenser energy went · into the filaments. From this we hoped tQ find conditions under which the filaments would vaporize completely. One way of characterizing the explosion involved the measurement of the initial and final condenser energies. A second way was to collect and examine the exploded metal. The filament is clampee..,.against a glass microscope slide, metal being deposited thereon after the explosion. The appearances of these deposits are similar to the photographs taken by Anderson and Smith 3 of exploding wires. B. Apparatus and Experimental Procedure 1. The surge generator In most of the experiments eight 25~microfarad Dubilinier condensers were connected in parallel. Across the condensers a semi-infinite resistance electronic voltmeter was placed. The readings on this meter were calibrated against a Weston precision voltmeter at the end of each experiment. The system was wired with coaxial cable (resistance= 0.01 ohm/ft., inductance= 0.09 microhenries/ft.). The condensers were connected to the central terminals of a number 3294 Leeds and Northrup pinch type double-pole, double-throw switch, the lower terminals of which were connected to the power supply and to the Weston voltmeter. The upper terminals of the switch were connected to the filament explosion unit. A three microhenry inductance was placed in series with the explosion unit in most of tbe experiments. 2 9 Preparation of the filaments It was felt that soldering filaments to leads is unsatisfactory because 1) solder does not wet tungsten, 2} solder frequently flows beyond the point where filament and lead meet, making the effective filament length and diameter uncertain, and 3) the filament may become fouled with rosin. The following procedure was adopted since it a) yielded satisfactory reproducibility of data, b) eliminated the above difficulties, &nd ij ) furnished quantitative agreement for data obtained using carefully prepared soldered joints and for c~pillary joints. Each end of the filament is inserted into a short piece of monel capillary, which is then crushed onto the filament using a flat-jawed vice or long Il;OSe ppliers. The joint is tested for mechanical contact by pulling the filament away from the monel ends; the assumption is made that good mechanical contact is a satisfactory test for good electrical contact. That this procodure gives reproducible results may be seen from the results for 3.1 mils constantan filaments for 50 pF and 1 pH. For minimum energy explosions the total energy dissipated in the filaments is o.240 and o.242 joules per centimeter for soldered and capillary joints respectively. The filaments used were the best grade metal wires which we could obtain. These were manufactured by Sigmund Cohn, Driver-Harris, and Callite. 3. The filament explosion unit The filament explosion unit used in most of the experiments is shown in fig. 1. It was constructed so that 1) it could be directly connected to a high vacuum system, 2) the filament would be supported vertically, clampedr against a glass slide, and 3) the electrical circuit around the filament would be a continuation of tbe coaxial leads. A large brass standard taper joint was constructed which gave a vacuum-tight seal with a glass standard taper joint. The glass was sealed to a mercury manometer and an oblique bore stopcock, beyond which were a series of standard taper and ball joints by means of which the system was connected to the high vacuum apparatus. Fig. I F";la~"+ ~~plosio"' -tf f it"'"e+us - - - - - - - T b Vac.UVffi S~s+•'-" --Oltli1,ue I.on 1topcoc.l< - --Mev-c.w-.!t ""'-."o~tev- ,, ' - - 'Two-•"cla cfa1111.p - - G-l-11s-ell\clostcl v~c.vv~ c4.a"''ev- - - Br"•ss tube CsJeleJJ.) - - Ci Iass h-1 ic. nsc.o pe. s /,"Je, , ' : - --Me.,._I wa;, wlticA surports s/iele - ••~•"'+- - Me-tat fi t,f stfte/1 J,-.~o.rw "t"' i s e.,(p( ode,,l Cla~p - - - - - - _ V.-cuu""' ~..-, fo"r" le•d (-Mis ~"~...,..., i11svla1-e, ~ ,_, e.kch-ice/!,'1tlf .,._,,_. - - - - - l?-roovtt. w" i cA seats 1,,-ass sJcicU- - -- - - -Co.,clvc.tor - - - - - ---O~r • - - - - - :"'si.la r•rc.ela; .... +uk lft.iJ of c..-aAia.l c.e/,/e Solcle~ -t. ~ J,.-auJoi11.-I: -Co-a1'i•I at~lt. wltfc." :,o•s 'Q> ~ douWe. ,-,~ douJ,/~ 1-ln•.v Swi-t-c/\ The outside lead of the coaxial cable was soldered to the brass joint. The inner lead went through a. hole in the center of the brass joint, being insulated both for vacuum and electricity, and was then soldered to a clamp. The jaws of this clamp were clinched about a glass slide (kept in place by two ways soldered to the brass joint), pressing the monel ends on the filament against the glass and establishing electrical contact with the filament by strong clamping action. A two-ended clamp was secured on the other monel end of the filament from the upper end of the slide. A heavy brass tube, the upper part of which was soldered onto flexible dome-shaped, copper mesh, slipped over the clamps, filament and glass slide and into a deep groove i~ the upper face of th~ brass standard taper joint, astablishing electrical contact therewith. The upper end of the two ended clamp was then clamped onto a heavy copper wire soldered to the center of the dome. When experiments were performed in atmospheres other than air, the glass standard taper was slipped over this assembly and connected to tbe vacuum apparatus. gases were used without further purification. slides were the ordinary microscope slides. Commercial The glass -14- c. List of symbols Explosion Process of blowing out filam~nt with electrical surge Filament The fine wire blown out by the electrical surge. 0 Length of f ila.ment ( cm) D Filam~nt diameter {mils, i.e. 0.001 inches) M Microgram atoms i n one cm of filament E Total energy dissipated in filament per cm (joules/cm) " e II It II {kcal/g.atom) E{analytical) E calculated by eq. land Appendix A5. E{grs.phical) E obtained by solving eq. 1 graphically. E 0 , E1 •rerms K The total energy dissipated in the apparatus (excluding the filament ) (joules), K = EF. ln the series, E = E 0 + E 1 .J Filament res ist.ance per cm { ohms/cm) Mean filament resistance per cm when there is no gaseous discharge {ohms/cm) defined by f- . s-t'OQ ( ~ - co -Co ( (E/2) jO' (1 r / when E/2 joules /cm has been added to tbe f' ilament 0 Tewns in the series, l = fo +(:} The apparatus resistance (ohms) , {excluding filament) This is taken as the values obtained in Appendix A5. ro, r1 Terms in the series, r :: r 0 -t- r1-f R Total resist&~ce of system, apparatus plus filament (ohms) F r/(°, cm F o, F1 Terms in the serie s, F Vo Initial condenser voltage before the surge (volts) Vr Residual condenser voltage after explosion (volts) =F 0 -r F 1 f -.1.0- Inductance of the system (microhenries) Capacity of the condensers (microfarads) Total energy dissipated (joules), i.eo the initial minus the final condenser energies. i Current,amperes) t Time after ~ffective initiation of surge (microseconds) texp tat which explosion occurs when there is no gas~ous discharge (microseconds) Constant s in eq. 4. Constants in eq o 8. Constants in eq. 11. z 0 , z1, z 2 are defined in eq. 6. These are defined in eq. 10. D. Expe~imental results The mechanism of the explosion that occurs when !in electrical surge is passed tnrough a metallic filament is complicated. In order to study some of the effects of the surge, four series of experiments were devised in which only one initial condition was varied throughout the series. Each series was repeated with a number of different metals and diameters. 1. Minimum energy explosions It appeared desireable to study experiments in which the states of the filaments at tbe times of explosion would be known. Although this was not feasible with the available equipment, a more modest aim appeared to be experimentally ache ivable. By using only the minimum energies necessary to blow out filaments it seemed reasonable to assume that the states of the filaments at the times of explosion might not differ much from each other as filament length is varied. a. Experimental procedure and precautions In order to find the minimum energy required to blow out filaments, repeated surges were sent through the system, each with more energy than the preceding surge (V 0 being increased by 5 volts) until the filament blew out. Quantitative agreement was obtained in experiments to see if six surges gave the same results as a single surge explosion. In some experiments, especially with 1. 0 mil tungsten filaments, V~ - V~ was less than (V 0 - 5) 2 , indicating that the filaments should have blown out on previous surges. discarded. These data were The difficulty may have · arisen from changes in shape of metal filaments as a result of repeated meltings 0 Helium was used in th~ cases of several metals which reacted with oxygen. Co Results When the total energy dissipated, AV2 C/2, is plotted against filament length, J, a straight line fit is valid within experimental error, as may be seen in fig. 2o The scatter at 50 pF' and 1 pH is seen to be appreciably less than at 200 p.F and 4 pH. These graphical results may be represented by equations of the form; = E (j-,. F) -- • • • • • • • • • • o • • o • • • • • • • • • • • • • • e ( l ) E, F, and Kare listed in Table I. The derivation in Appendix Al shows that if we assume that the surge energy is dissipated uniformly along the filament ( and "hot points" are also well distributed), we may interpret E, F, and K rather simply. Eis then the total energy dissipated in the filament per cm, F the ratio of the mean effective apparatus resistance to that of the mean filament resistance per cm of filament, and K the total energy dissipated in the apparatus (excluding the filament) 0 This interpetation is strictly applicable to the quantities in Table I only if E, F, and Kare independent of filament length. The effects of inductance and capacity are summarized in Table II. More experiments are obviously needed to clarify the situation. Since we have been unable to correct the results at 50 JJF for variation with filament length, we may not conclude that the blowing out temperatures for minimum energy explosions are higher at 200 pF and 4 pH than at 50 fa' andlpH. 0 ,.r ,.• I d./--...-or"'"'' 2•• _,µF -4jlH ·' N ic.kel -(ila""e"'+s 0 ,s ,.2 z.o t.o (j) "I.O <D ,.o il 19 I A+....,.osphe-re.. o Cu Al,,. ......... ls e e ,.0 IP Pt A·,r .. .... ••► A9 A,r .i , c.1n 10 3.0 2 .0 1.0 <!J .:e ~ • Au A'1r + ,.r """'"' .... ).0 • ~.o a hz. HeliuW\ ~ .....,,,.. ~'"'"' a,. 2..0 TuNGST£N Fi la 4-/A- H • • en f-.s Heliu"'1 - , Ai:-mo phe.Y<1 200 rF 3,0 ,.s _ 2.S" To fa/ e11ev-~'.i d,'«ipafe.l vs. f;!a .... e.at l<"'JtJ, for ~jV\j~v"-'\ ~-J-1 •• e"'~".j:' e.xr/os,'0'15, S'Of'F, (1JrH 2.0 Air,/ a+..,ospA<-v-e. ~ ,iovles ;i,_ , , /.S - /.0 /.0 As 0 Ao+ Co4 Ni• 1"t a Fig. 2 3.0 ... o TABLE I. Graphical results of the experiments at atmospheric pressure in which the minimum energies for rupture have been used. Experiments with constantan filaments are given in Appendix D. Filament Metal D, mils Gas E, e, F, ioules kcal cm cm g.Ettom K, joules texp/R, microseconds ohm C: 50 pF, L = l pH, texp/R calculated from graphical results. Air 0.138 7.41 l 050 0 .207 105 Au Air Ool57 8.9 6 0.92 00144 155 Cu Air 0.212 7 .4 0 Ni Air Pt Air Ag 3.0 130 157 o.283 13o5 139 C = 200 pF, L: 4 pH, texp/R calculated from analytical results. Ag 3.0 Au Cu 3.1 Air Ool47 7.88 256 Air Ool73 908 8 313 Air 00285 9095 305 Fe Helium (0.60)(21.1) 0. 06 ( 0 0 036) 278 Ni Air ( Oo35 )( 0 0 032) 288 Air & 0 0 247 19ol Oo25 0.062 324 Air & 00472 16o2 0.41 Ool93 285 Helium Helium Air 5.0 0.857 1606 390 Air 1.00 o.gs 495 Air 0~85 1 0 24 371 Pt Air o.46 o.175 311 w Helium Ool40 63.0 Helium 0.487 4lo5 (0.06)(000084) 292 270 Oo59 0.41 351 424 TABLE II. Comparison of graphical results of Table I to show the differences between the results i;i.t 200 pF and 4 / uH and those at 50 JJF and 1 JJH. Filament Metaf9j, mils E(200 ;$) F(200 pF) K(20?) ~ t ~R (200 l:§.:) E( 5~ ) F( 50_/JF) K( 5 ) exp R t5OJUF} Ag 3 0 0 lo06 lo73 lo84 2 0 44 Au 2o9 1.10 1,83 2 02 2o02 Cu 3ol lo34 lo35 1.s1 2.35 Ni 3o0 lc41 0068 o.97 lo82 Pt 3.0 (lo34) 0~74 loOO 2 24 0 0 texp/R has been calculated by means of the equation in Appendix A3. The differences between the explosion times per ohm at 200 pF and at 50 pE are mainly due to two factors. The ratios of the capacities, 200/50, contributs a factor of 4o Since the initial voltages at 50 pF are about double those at 200 )iF' for comparable conditions, the ratios of the logs of V /Vr contribute a factor less than unity. 0 It is seen in Table II that the combination of these two factors results in a series of ratios of the order of 2, So far eq o (1) has been solved graphically. In order to correct E, F, and K for th~ effects of variation with filament length, an analytical method bas been developed to solve eq o (1). 1~e whole procedure of using eq. (1) is an indirect method of obtaining our desired results. If more equip~ent were available we would be able to measure the volts.ge and current a.s functions of time, thereby obtaining the energy input into the filaments more dir•ectly. In the analytical method we solve eqo (1 ) by assuming a) that I: l(E/2), i.eo that the mean filament resistance may be adequately represented by the filament resistance when E/2 joules/cm has been dissipated in the filament per cm, and b) r is proportional to the square root of the frequency (skin effect relationship), and that for our overdamped systems the time at which the current reached its maximum value is an adequate relative measure of the frequency, being inversely proportional to the frequency, and the correct order of magnitude of r is obte.inable from the graphical results (i.e. the curve is passed through an experimental point, cf. fig. 7 in Appendix A5). Calculations are made by successive approximations until E, r, and f' are self-consistent. -20- The analytical calculations have been limited to the data at 200 r,F and 4 pH. The uncertainty in the inductance for the data at 50 pF and 1 µH makes the skin effect corrections unreliable. The individual experiments at 50 p in Table III, and those for 200 pF in Table IV. are given The analyt.ical averages for 200 pF are given in Table V and compared with the graphical values of Table I in Table VI. These analwtical averages have been made by neglecting experiments with very short filaments. Quantitative correlation is obtained between e (graphical) and e ( a.nalyt ical) when e (graphical) is corrected for variation of E and F with filament length (cf. Appendix A4) for the six nickel filaments, go ld and silver, but not for one tungst en filament, iron, and copper 0 For the latter experiments these discrepancies may be due to lack of sufficient data to eva.luate all the quantities involved accurately or to the failure of the mean resistance hypothesis. For the case of an alloy 1 ilrn constantan, the mean resistance hypothesis sould obviously be inadequate for large E ranges. Now that the data may be satisfactorily interprated we will consider some of the results of the analyt ica.l calculations. (1) Total energy input into filament per 00ntimeter 0 Fnr minimum energy explosions, Eis seen to vary with D, £, s.nd filament meta lo effects of C and L. ~le have already discussed the Nickel filaments showed no differences in behavior when exploded in air and in helium at e.tmospheric pressure. TABLE III. Minimum energy explosion data for 50 pF, 1 and air at atmospheric pressure. p., texp and texp/R ha.ve beem calculated with graphical values of R. Filament Metal D, ), cm VO' Vr, volts volts joules mils Ag Au Cu Ni Pt 3.0 2.9 3.1 3o0 3.0 4v 2 c , t exp' 2 usec. texp/R, usec/ohm 0 0 50 105 5 00275 • 0 1,55 130 15 00417 38 104, 2.00 140 20 00480 40 96 6085 215 10 1.15 115 116 Oo25 85 0 0.181 - 0.87 105 5 00275 45 136 4o00 1?5 5 Oo76 160 Oo6G 135 5 o.455 - 174 lit70 165 33 Oo65 33 82 3o25 200 5 lo00 107 178 5 0 20 243 35 1.44 81 96 8010 285 10 2.03 199 165 Oo75 130 10 00420 139 127 lo35 165 7 0068 249 157 3ol0 220 7 lo21 448 172 6.80 315 10 2.48 1038 172 o.s3 125 5 00390 221 160 1 0 45 155 5 Oo60 238 121 7o06 295 20 2.17 985 135· e TABLE I.V, Results of minimum energy explosions at 1 atmosphere, 200 fiF, and 4 JUH. Filament Gas Metal D, J, cm V , vr, v8lts volts mils 4v 2 c ~, e, E, K, texp' texp/R, Regions joules kcal joules of joules cm g.atom psec psec/obm constant e,"x" Ag Au Cu Fe Ni 3o0 209 3.1 3.1 1.2 2.0 Air Air Air Helium Air Air Helium Air 3.0 Heliu.rn Air Air Helium Helium Air 4.0 5.0 6.0 Pt w 3,0 1.0 2.3 Air Air Air Air Helium Helium Oo51 70 1.62 80 2.80 90 3.95 105 10 20 ~3 39 Oo48 0.60 o.s1 Oo95 0023 5 00149 Ool50 0.139 12.6 8.0 800 7o5 o.39 0.40 Oo62 70 1.22 75 2.28 85 2,92 90 4068 105 20 24 21 10 2 Oo45 Oo50 o.68 Oo80 1.10 Oo44 00181 o.169 0.170 0.165 25. 10.2 906 9.7 9 04 o.68 90 2.28 115 3.23 125 4.79 135 19 34 25 22 o.77 1,21 l o50 lo77 o.332 o.275 0.273 0.242 0.70 80 1.38 95 2.04 110 2ol0 120 2,80 135 5 2 4 42 24 o.64 o.9o 1.21 1.26 1.76 o.36 Oo36 X X 161 211 X Oo18 0.29 0.30 0.30 Oo33 215 131 217 392 250 234 278 427 X X 1106 9.6 9.5 8.4 0.$5 Oo58 0.61 o.63 130 163 265 361 317 243 319 353 o.56 o.53 o.54 Oo58 19.4 18.5 18.8 20.2 0.134 Ool28 0.131 0.143 ... ... ... 1100 2380 211 345 * 30 40 57.5 0 7 20 0.090 o.1ss 00291 0.12 0.10 0.09 2 26 23 20 0.0074 000107 0.0160 o.63 Oo93 1.20 1.92 2,29 2,99 55 55 60 75 80 80 6 11 Oo30 0.29 o.36 o.54 0 0 62 o.63 o.4o 0.26 Oo25 0.25 0.25 0,19 310 19.9 19.6 19.6 19. 0 14.9 o.~50 0,049 00053 0.053 0.046 o.os2 Oo53 01155 Oo45 Oo47 Oo44 o.46 18o4 1808 15.6 16 1 15ol 16,0 0,18 0.16 Oo20 0.22 0.23 0.25 15 14 11 25 3 24 23 387 300 <it Oo69 1,37 3,00 4 145 144 - - - - X X X X X X X X X ... 4070 4630 365 211 1270 846 432 302 1700 2120 2720 322 347 397 217 . 219 491 766 275 312 960 269 X X 285 255 524 X .. ... X X X X X X 0,60 75 Oo69 75 1.43 95 2.00 110 2.49 115 3,11 135 · 35 Oo50 Oo56 Oo84 1.16 1.32 1.70 0,58 85 1.21 115 2,98 165 3 •I7 170 21 32 12 0 0,68 1.22 2.71 2,89 0.52 0.62 o.71 0,72 10.1 12.1 13.7 13.9 o .37 o.44 o.so 0.61 160 233 1010 ii, - 0,20 100 0 .. 81 135 1.99 170 2.69 190 3.08 200 28 20 27 9 8 0.92 1.78 2,82 3.60 3,99 o.74 o.95 o.87 o.91 0,91 9 .2 11,8 10,8 11.3 11.3 o.78 1.02 1.11 1,13 1.19 90 210 335 688 810 273 376 365 601 637 0,32 105 0.50 140 o.7o 150 o.79 160 1.00 165 2.39 220 2.54 225 0 18 21 20 35 50 28 1.10 1,93 2.21 2.52 2.60 4,59 4,98 0,50 0,90 o.92 1.02 o.97 1,09 1.15 4.3 7.75 7o9o 8,80 8.31 9.37 9.85 0.92 1.47 1.58 1,70 1,59 2,00 2.08 163 183 150 230 334 403 389 413 317 295 408 X X X X X X 0.32 60 1,21 80 1.30 85 2,38 105 20 21 10 4 0.32 0.60 0.11 1.10 o.38 0,43 o.39 17.9 20,3 18.6 0.142 o.156 o.175 340 860 193 429 X X X 0,72 1.90 35 55 18 10 0.09 0 0,29 * 0,60 70 1,39 95 1,98 110 1,99 110 14 27 26 25 0.47 o.83 1.142 1,15 0,54 o.53 o.53 46.l 45.2 45,3 0,076 0,091 0.092 1520 2420 2510 251 288 296 443 231 378 2 * 0 .. ..148 • - X X X X X X X X ... . 223 340 ~I- * - 3.0 Helium 0.60 90 1 .10 115 2.38 145 10 36 22 o.so 1,19 2.05 1.07 0.91 0,78 53.7 45.3 38,8 o.1s8 0.197 0.210 1010 702 1960 4.0 Helium 0.70 120 1 ,50 165 2.20 185 5 20 13 1.44 2,68 3,41 1,40 1.42 1.28 39,4 39.8 35.9 o.46 0,55 0.60 908 1440 * Resistance data are not available in this temperature range, ... . 424 529 ·x X X X X TABLE V. Aver~ges of the analytical results for minimum energy explosions a.t atmospheric pressure in air and in helium for 2 00 pF and 4 pH. The averages of texp/R have been presented in Table I 0 Filament Met:..! D, mils e, kcal Average s tate of Mean devia- filaments at time of explosions. g.atom tion in e, F, cm K, joules % Ag 3.0 7. 84 56% ± 9% melted 2 06 Au 2o9 9o72 88% ± 8% melted 1<>8 Cu 3.1 9.19 70% :t. 16% melted 203 Fe 3.1 19.2 Liquid at 2010:t'74°K 0 24 3.0 15.7 s. o w 0 Liquid at i 2420:tl80°K 0 0 14 Ni Pt 0.61 Liquid at 2190~40°K 0 0 20 Liquid at 175 0±40°K 0 0 49 45% + 19% melted 0 0 81 0% ± 5% melted 1 0 24 0.05 0 Solid at 1400 -t l 00°K l ~ 74 4. 8 Liquid Liquid Liquid Ool6 TABLE VI. Comparison of analytical and graphical results for minimum energy explosions at atmospheric pr·essure, 200 pF, and 4 plio Filament Metal D, mils e (gra!hical) e(ana ytical) l e1 (l t- F) e ( gra!h ical) e(ana ytical) "" e(analytical) Ag 3.0 1.01 o.97 Au 2.9 lo02 1.00 Cu 3ol 1.08 1.15 Fe 3.1 1.10 lolO Ni lo2 o.93 1.07 2.0 Oo98 1.05 3o0 lo03 o .95 4.0 lo26 Oo97 5o0 lo07 o.gs 600 lo45 1.02 Pt 3.0 (Oo96 }@ ( 0.90)@ w 2 03 Oo91 Oo92 4.0 (0.92)t@ (0.82)@ @ These ~ F1 values are unreliable on account of graphical uncertainty 0 It is seen in Table V (and also in Table I ) that e decreases for both nickel ~nd tungsten as filaffient diameter e, loge, and 1/e were each plotted against is increased. each of tbe following; D, log D, 1/D, and D 2 o Tbe most satisfactory linearity was obtained by plotting e against either Dor log D (cf. fig. 3). The equations of these lines are; Ni: and e :: ... 10 2 log M t- 24.,4 W: and e c - 12.9 log M -t 51.,6 0 (2) where e is in lrnal/g.a.tom, Bin mils, and Min ug. a.toms/cm. The results for nickel are more reliable than those for tungsten. Difficulty was encountered in obtaining the tungsten data. For example only two out of fifteen explosions satisfied the condition that E~ - E~ should be greater than The cause of this behavior is not known. A possible interpretation of the decrease of e with increasing Dis that a large part of e goes into overcoming some surface phenomena, since the surface are~ per g. atom (for a cylinder omitting its ends) decreases with increasing D. We have already seen (page 9) that explosion properties of at least some filaments can be cb&nged markedly by slightly amalgamating the surfaces of the filaments. Gaut ion should be exercised in the interpretation of the results for large diameters. It will be seen further on as well as here that most of the phenomena studied for the large diameters behave differently than those for the small ones., Anderson found that it was not possible to obtain good effects with wires larger than 5 mils out at high voltages 0 ) 0 (His experiments were carried In our experiments we find (cf 0 Table V) :;: ~ ! ~ J g-, t ---~ ..._, l '.:i: i ! + - Jf Cl> .,y ~ J V ): l . J ~ ,., 0 '$;_ 0 2 ... .. ,-.. "' "' ,,. "' ~ I r- ..t " .... 0 0 . ~ that the average state of 6.0 mils nickel filaments at texp is that of a solid and of 5.0 mils a solid at the melting pointo We will now examine the effect of filament length one in the regions of constant e. that e : f. e 0 -t e 1 It will be assumed It is seen in Table VII that e 1 increases with increasing M. against Mon semi-log paper. In fig. 3, e 1 is plotted The equation represented by the line is; ..•.......••....•......•••...•.••• ( 3) = It is interesting to note that e, e 0 , and e1 may be considered to be proportional to log M. In Appendix B, it is found that both log rand log r1 are proportional to log f(analytical). (r 0 is a constant equal to 0.27 ohms.) (2) End effects (Behavior of very short filaments) If the results in Table IV are examined it is seen that some of the numerical values of E for short filaments are considerably different than those for longer filaments. The ratios of the results for short filaments to the values they would have if there were no end effects are given in Table VIII, and the trends in these results are summarized in Table IX. The results for .J,= 0.20 and 0.32 cm (two experiments) are tentative since there tire not enough data and'tbe error in determination of filament length is relatively large in these two exp~riments. Since r does not exhibit any significant end effect, it is probable that the end effect is mainly a filament phenomenon (and therefore affects the circuit only indirectly). TABLE VII. Effects of filament length one in regions of Filament Metal EB•atoms cm M, u constant D, mils Ni e" for the data in Table IV. e1, kcal goatom cm kcal goatom - 1.84 w Ni eo, er ( J+- F. ' ) eanalytical) - 0.20 47.8 • 0o05 2.0 Au ... 0o09 Ag .. 0ol5 Pt .. 0.04 Cu - 0o43 ... 0.01 Fe Ni w Oo50 0.02 0~02 o.oo Ni Ni Ni TABLE VIII. Data of Table IV for short filaments are compared with the extrapolated analytical values. Filament Metal D, M, mils e:g. at oms ;_, cm e eo -t- e1e §. r foi+r ,1 ro+ r1{ F Fo+ F1£ cm 1.1 Ni 1.2 o.69 1.08 lo28 loO 0.78 3.1 Ni 2.0 o.63 lo54 1.52 0.94 0.62 4o2 Au 2.9 0 0 62 2))·54 4.13 1 .13 0.26 4o4 Ag 3o0 0.51 1.51 l-042 1.00 o.7o 6.8 Cu 3.1 o.68 1.12 1.07 1.00 o.93 6.9 Ni 300 0.60 1.17 1.os o.97 0.90 0.69 1.20 lo09 0.87 o.so 805 w 4.0 0.10 1.00 1.00 1.00 1.00 12o3 Ni 4.0 0.58 o.99 o.93 Oo94 1.01 19.2 Ni s.o 0.20 o.s1 0.90 Oo90 loOO 2767 Ni 600 0 0 32 o.ss 0.86 o.93 1.08 o.so 1.03 o.99 o.96 o.97 0.10 1.05 1.00 1.00 loOO TABLE IX. End effects (results for short filaments) are summarized for 200 pF and 4 JiB-o Filament length range, cm 0.50 ~ _f ~ o. 70 cm M range, pg.atoms/cm <7 >B 19.2 & 27.7 Reliability of results Valid Valid Not established )1 =1 <1 Average values 1.,44 1.02 0.,70 R&.te of change with respect to M <0 =0 (0 )1 : l < 1 Aver&.ge values 1.66 0.98 0.,88 Rate of change with respect to M <: O =0 ~o Scatter about unity =l <l ( 0.99) o.98 Oo92 < l : l )1 Oo71 1.00 lo04 ... 0 ~o e eo +- "1..f ~ ,,.t+r,J2 r ro + r1~ Average values F F o + F1,( Average values 0.20 & 0.,32 cm Rate of change with respect to M < O (3) Times at which explosions occur. The values for texp have been calculated using the results in Appendix A3. These values range from 90 to 4,630 microseconds for the minimum energy experiments in Table IV. The results for experiments with Vr less than 5 or 6 volts have not been calcul~ted since there was a condenser · lag of a.bout 2 vol ts f Ol' small voltages and since instrumental sensitivity was poor for very small voltages, probably of the order of several volts. In addition the mean deviation in texp corresponding to the mean deviation in e becomes very large for these small Vr (cf. Appendix C). It is seen in Table IV that texp increases in most cases with increasing filament length. texp/R and texp// are both almost independent of filament length. Whereas the values of texp/J.. for different metals and di~meters vary from 65 microseconds per cm for silver to 1540 micro- seconds per cm for 1.2 mil nickel, the va l ues of texp/R vary from 270 microseconds per ohm for 2.3 mil tungsten to 495 for 5.0 mil nickel. Averaging over all the metals, we get for texp/R in regions of constant e for M < 7 pg.atom/cm, 295psec/ohm ± 18%', and for M) 8 pg.atom/cm, 424 -t- 20%'. both regions overlap. large scatter. The values for The end effects are m~sked by the If we assume that there is an indeterminancy of about 4%' in e in the blowing out process, then we get a corresponding scatter in texp of about 20%'. discussed further in Appendix c. This is 2. Moderate energy explosions Three series of experiments follow in which moderate energies have been used with C : 200 F and L In ~ 4 Jili• the first series, all the initial conditions have been closely reproduced with the exception of gas pressure. a. Effects of v:..rying gas -pressure A series of explosions were carried out using 2.0 cm lengths of 2.9 mil gold filament and V0 : 200 volts. (This voltage gives a small excess of energy over that required to completely vaporize the filaments, if such a process were to occur without prior rupture.) The results in Table X show that for two large pressure ranges which overlap considerably the residual voltages remain about constant independent of pressure changes. These two pressure ranges overlap f ram about 50 to 135 mm. In this region either one of two processes occur, either the f ilaru~nt is ruptured when it is 4 to 20% vaporized or the co~dens e r is s lmost comple tely discharge d. The latter precess does not preclude the possibility that the first process occurs , fallowed by a ga seous discbarge. A s e cond interpretation of the almost complete dis charges is that the filament is about 100% vaporized at t e xp• In this case the results of Smith which we have summarized on page 7 are pertinent since they would guarante e a sharp break in the electrical circuit for our conditions (small Vr}o Further experimental work will be need to find out which interpretat i on is correct 0 If a gaseous discharge occurs the calculated value of e may not be ev e n of the correct order of magnitude sinc e the r esist ance cf a gaseous discharge is non-Ohmic {and unknown for our system) TABLE X. Results of explosions using 2.0 cm lengths of 2.9 mil gold filaments at Vo= 200 volts, C: 200 pF, and L : 4 pR. at a number of different pressures. The columns B through K have meaning for the first 12 experiments only if no gasecns discharge occurred. Pressure, Vr, AV 2 c e, % Plates K, mm v o l t s ~ , koal Vapnrized joules joules g.atom at texp Gas 22 Air 0.58 21 20 3.96 100.2 10006 6 17 3.97 100.0 9948 7,8 40 3.84 Ammonia 48 3o77 lOOoO Oxygen 48 97 3 0 40 102 .6 97 0 2 96.7 51 9,10,11 39 58 135.2 3 0 84 97o5 12,13 50 0 4@ 277 Air @ For 40 1 o.2e 97 0 3 162 lo38 32 15 16405 156 lo57 36 18 17,18 212.5 161 14 19 35203 157 17 573.6 162 1.38 32 169 1.14 26 this experiment, V0 :: 14,15,16 Oo27 11 20,21 300 voltso Explosions with 2.0 cm lengths of 3.1 mil copper filaments. Ammonia 8lol 142 Ammonia 242.7 153 ~ ~~ 1~•~6_6_ 1.98 - ~ v,.... In order to make calculations the resistance data haye been extrapolated above 1aoo°K. Even though the calculated results may not be quantitatively correct, the results should be good enough to reveal the main features of the data. (The experiments at 10 •"~ mm which give the state at explosion as 99% vaporized, assuming no gaseous discharge, do not require extrapolation of the resistance The spectral studies of high energy iron explosions data.) performed by Anderson (cf. page 8) show that at different pressures the spectral characteristics change, the pressure regions show a striking similarity to those which we have The main features are listed below; pressure, mm 10·4 to 3 20 50 to 135 150-760 Vr,volts 2'0 40 46 & 162 161 11v 2 c joules 3o96 3.84 3o78 & 1 0 36 % vaporized 10~ 95@ 92@ & 14 Fe spectra . Emission t exp, psec 1690® found. ~' at texp @ texp/R,µsec/ohm 460 Largest ball 3 sizes on slides, microns @ These ... Appreciable continuous background & reversal Continuous background. Only absorption lines. 1290@ & 104 105 294·® & 42 43 11 & 28 100 values are valid only if it is shown that gaseous discharges do not occur. The appearance of the deposits in high vacuu.m indicates complete vaporization (whether or not accomplished directly or by gaseous discharge). These deposits are transparent and are green to transmitted day light. As pressures are increased the density of deposit increases In fig. 4 we show the results of the calculations assuming no gaseous discharge. We shall not try to give arguments to show whether or not the filaments are completely vaporized since none of these have been decisive. In the plates which follow we have presented typical slid~ in the different pressure groups both at low and at high powers. One feature that distinguishes the study of the metal slides from that of high speed photographs is that, although they both look alike at low powers, the metal slides may be studied further at powers for details such as ball size. (We do not wish to imply here that the significance of the metal deposits is the same as that of the photographs but that they do frequently have a similar appearance.) /00 0 0 0 0 0 00 0 "i" ~ vapor i ~4-J-iot'\ 8 a-J- e.~p/osiotl') 8a 70 F i!J, 60 °PE. -rc.e 60 If ~+ Va f' oY' i ~if 1-i o"' vs. boi /;"'-' ro;,-,.t- of +~e 9 o Id f; I a "" e ~ +s. 30 2.0 0 0 0 0 0 IO :BoiliY19 point of sold. ar pressuv-e of S!Jsf,:"'} 1< 0 O 1500 17so 2000 2250 2.St>O 2'/SO 3000 0 3250 Plate 2. 4.7x Plate 3o 632x 10-4 mm of Hg, cf. Table X for further details. Most of the film is transparent and appears green with transmitted daylight. film was smooth. At high power, most of the The central metallic region has been photographed since it is only here that details were observed. The streaks on plate 3 are attributed to motion of tiny globules of metal along the glass. Plate 4. 4.7x Plate 5. 4.7x Pressure; 10.. 4 mm. Plate 4 is similar to plate 2 at high powero The slide was wiped vigorously with lens tissure to see how much of the deposit adhered to the glass. It 1 is apparent in plate 5 that the translucent films were wiped off but the heavier deposits were not. Plate 60 4.7x Pressure; lnnn The appearance of this plate is less cloud-like than the appearances of plates 2 and 4. This plate is comparable in appearance to parts of plate 7 and 8 0 Plate 7. Plate 8. 632x 4.7x Pressure: 2.6 mm This slide appears to be different at low powers than plates 2 and 4. become small. At high powers the differences The essential difference appears to be in the thickness of the deposit. Plate 9. 4.7x Pressure: 102.6 mm On this plate there is a well defined central region which has the appearance of a slightly crumbled wire. This space is empty when looked at through transmitted light. Photographs at 632x are shown in plates 10 and 11. Plate 10. 632x Plate 11. 632x The background in plate 9 has no prominent globules of metal. In plate 10 we apparently have a portion of the original filament which did not vaporize completely. It appears as if the filament moved from one position to another during the vaporization or rupture processes. In plate 11 we show the occasional irregularities in the background. Plate 12. Plate 13. 4.7x 632x. Pressure: 135.2 mm Although similar to plate 9 at low power, difference appear at high power. central axis are large. The balls at 632x along the They are located at the end of streaks (the formation of these streaks are undoubtedly due to motion of the balls). scattered about. There are larger globules Plate 14. 4.7x Pressure: 9703mm Only the regions where the filament was clamped to the slide show prominently. Photographs at 632x are shown in plates 15 and 16 0 Plate 15. 632x Plate 16. 632x Plate 15 has been taken at a boundary between bright metallic deposits and fine vapor deposit of plate 14. The balls are distinctly larger than any observed in preceding plates. Plate 16 shows an area similar in appearance to plate 13. Plate 17. 4.7x Plate 180 632x Pressure: 164.5 mm The surface of this slide was wiped vigorously with lens tissure. The vapor filmr-1has been removed (as is evidenced by the non-reflecting dark background), only the large deposits have adhered strongly. The 632x slide was photographed before the slide was wiped. The large ball is about 100 microns in diameter. Plate 19. 4.7x Pressure: 212.5 mm The black streaks are dark translucent deposits which appear green with transmitted light. If plates 2,4,6,7,9, and 19 are examined, it is seen that these black films are prominent for pressures above 1 mm. At lower pressures the films appear more metallic. Plate 20. 4.7x Plate 210 632x Pressure: 1 atmosphere. The filament appears to have been bent vigorously during the explosiono b. Effects of varying initial condenser voltage. The experiments discussed in this section were run in air at atmospheric pressure using 2.0 cm lengths of filaments. When Vo is plotted against Vr, cf. fig. 5, it is seen that these two quantities are directly proportional to each other over a Vr drops sharply for low voltages at large range of Vo. which minimum energy explosions occur, this possibly indicates that rupture processes at moderate energies are different than those at lower energies. At high initial voltages, Vr drops sharply on account of gaseous discharges. The equations of the straight lines in fig. 5 are of the form, Vr : Al (Vo• A2) ••••••••••••••••••••••••••••••••••••••(4) Ai and A2 are listed in Table XI. The graphical scatter for the tungsten experiments is large. has been encountered before. er. pg 0 (Trouble with tungsten 21) On plotting M against A2 it is seen that satisfactory linearity is obtained. From fig. 6 we obtain l. For W; A2 For Ni; A2 :: 71.3 4fi M2 - 36 l. 30 0 4 M2 - 7 ························••0••··(5) The situation with respect to A is not as simple. Apparently 1 A1 increases with increasing M for small M, becomes constant for values of M from about 3 to 7, then decreases with larger M (becoming less than unity only for M greater than 8). The values of both A1 and A2 from Table XI are seen to depend on the metal 0 If Vo is increased it is seen in eq. 4 that unless a new phenomenon occurs, a voltage will be reached at which rupture takes place without any energy input. In several experiments we have been able to get within about 10 volts of these points but gaseous discharges obscured the results .,., 0 - I> A9 QAv • C:v + Fe V,-., 1/olts X»t 200 +t.'2.-ils • 2,o-.; 1, O 3,o """';/, Vr, volfs '"' '" + 100 . I- + X * Vo, volts •so ,oo ISO \/.,volts 0 . + , .. ,.,, 300 ,.,, Vo vs. V,- . , . v~, , + O 1.0 ...,;Is 2,3 ....,.;Js 0 3.o""'-;ls • lf:o ....,;Js 6 ,.o...,;/5 Cohclifio1,s VijrieJ •""- Vo, D, ~•.J f;/•,..•><f ~•+..I. I ,,f= 2. 0 c.., C=zoo/'.F volts 0, Tun9st:eri filame rs I / I ;o for ex.pe.ri.,...e.O\-t-..3 i" whic.l, -the o>,b ;.,;f;;;,/ + ,t/ / /+ I I /., L=11-/'H I ·. 200 2.-0 300 TABLE XI. Summary of results of moderate energy explosions in which the initial voltage is varied and filament lengtb(2.0 cm) kept constant. 200 pF, 4 µH, air at atmospheric pressure. Filament -Metal D, mils Al 4 K, A2, - zo, z 1xl0 , volts joules joules joules volt Ag 3.0 1.06 48 o.39 0.325 54 0.06 Au 2.9 1.06 42 0.21 0.234 47 0.06 Cu 3.1 1.12 74 o.s7 o.63 93 o.13 Fe 3.1 1.34 92 0.13 o.s2 165 o.4o Ni 1.2 1.10 23 0.013 o.03s 28 0.10 2.0 1.15 42 0.061 0.198 56 0.16 3.0 1.16 72 0.23 o.46 97 0.11 Pt 3 0 0 1.19 72 o.47 102 0.21 w 1.0 1.06 17 0.020 19 0 . 06 2.3 1.30 81 0.085 o.so 137 0.34 - - - - - - 300 1.33 119 Oo24 1.38 210 01138 4.0 (0.98 151 o.s2 1.40 145 -0.02 ) 6.0 0.71 275 1.24 2.53 139 -0.25 . - -z2x1of , joules volts2 at the points themselves. Experiments could be run with more equipment such that current and voltage would be measured as functions of time. This might yield information as to what kind of new phenomena arise as the voltage is increased past this point. In this way we could find out if there are any fundamentally different processes occuring at very high voltages (used in the experiments discussed in the appendix) and at the moderate voltages used in the present experiments. We will now examine eq. 4 to see what its consequences are. It is seen in Table XII that the energy dissipated in the apparatus, K, is constant for a given filament (excluding \ a few of the extrapolated calculations), and in Table XV that the numerical values of the averijge Kin this and in the next series of ~xperiments and the averages for the minimum energy explosions all have about the same value for a given filament. The assu.~ption of constancy of K will be discussed further in connection with Table xv. Combining the assumption that K is constant and that the filament length is constant (2.0 cm) with equations 1 and 4, we obtain, E = Zo+-Zl Vo -rz2 vi where z 0 • - ( AfA~C/2 -t- K )/} z 1 • A~A 2 c/) z 2 : -½(AI• l)C/~ Thus when experiments are carried out so that the only initial condition that is varied is Vo, then the result, eq. 4, implies that E is given by the simple second degree polynomial of eq. 6. The effect of filament diameter one may be clearly TABLE XIIo Results for moderate energy explosions in which Vo is varied for 1: 2.0 cm, air at j atmosphere, 200 uF, 4 uH. ~v 2 c Filament ~' cm Metal D, mils Vo, Vr, volts volts K, e, texp vr/ ~, joules 'kcal 2 R , volts/cm, for goatom joua.es E,S0C gaseous oh"' dis charges o Ag 2.00 2.02 lo94 110 200 300 65 165 267 o.79 10o5 lo39 1.96 27.1 (40) o.39 o.37 ( 0.42) 119 45 25 3.0 Au 2.9 1.98 2.00 2.10 2.00 2.00 105 200 300 325 340 67 169 274 300 311 o.66 1.44 1.49 1.57 1.90 10.7 26ol (34) (37) (46) 0.29 0.23 (0.26) (0.27) ( o.3o) 99 34 18 16 18 Ou 3.1 2.00 2.00 2.00 1.99 2.01 110 150 200 250 300 40 87 146 199 253 lo05 1.49 1.88 2.28 2.60 8.7 o.55 0.52 16.8 23.6 o.53 (29.2) (0.61) (33.6) (0.66) 215 115 66 48 36 Fe 3.1 2.04 1.99 1.95 1.95 2.01 2.02 1.97 1.91 110 125 200 215 225 250 275 300 4 46 146 165 62 65 74 64 1.21 18.5 1.36 1.87 1.90 ·:t 2.02 2.00 1.89 1.99 1.98 50 70 100 150 200 7 50 87 138 100 Gaseous discharge 2.0 2.02 1.92 2.00 1.96 2.00 1.98 70 75 100 150 200 250 28 15 67 125 184 230 o.41 ; 0,54 o.55, Oo69 o.61 0.95 13.9 (19) ( 19) (24) (21) 34.6 (0.050) 183 (0.060} 321 (0.861) 79 ( o. 063) 36 (0~065) 17 0.062 16 3.0 1.96 125 200 250 300 59 150 204 51 1.21 1.75 2.09 (17} (26) 33.3 {q 0 22) (0.24} 0.23 Ni 1.2 lo96 1.92 2.00 0.13 ** * Gaseous discharge ** . 204 63 52 31 32 38 34 Gaseous discharge Gaseous discharge Gaseous discharge o.245 (25) 0.240 (25) 0.241 (26) o.340 35.6 ( 0 .014) (0.014) (0.011) 0.013 Gaseous discharge 67 28 17 50 150 58 41 26 TABLE XII. (continue d ) Metal D Pt w 3.0 1.0 2.3 3o0 4.0 6.0 ~ Vo 1.92 2.00 2.01 1.90 1.99 1.98 125 160 200 225 250 300 62 107 150 63 51 64 1.18 * 1.41 * 1.75 * * Gaseous discharge Gaseous discharge Gaseous discharge 1.90 2.00 2 .oo 2.00 1.99 2.00 2.00 55 50 67½ 100 150 200 300 10 35 51 89 140 194 64 0.29 * * 0ol3 * * 0.20 * 0.21 * 0.29 * 0.23 * * Gaseous discharge 71 56 23 14 6 2.00 1.98 1.99 1.96 1.91 2.00 1.92 1.94 100 110 110 120 140 150 170 200 54 26 25 49 78 93 110 57 o.,ao 27o2 00070 1.14 Q.090 45.2 1 .15 45.3 0.090 1.20 48.2 0.091 1.35 (56) 1.38 (57) • 1.68 (70 ) Gaseous discharge 123 288 296 179 117 96 87 2 .03 2.01 2.06 2.01 2.04 150 175 200 225 250 30 83 106 140 79 2.16 47 0 3 0.24 2.38 * * 2.88 * * 3.12 Gaseous discharge 321 149 127 95 1.90 2.00 1.96 1.98 2.00 2.01 1.94 1.98 1.91 2.00 1.96 1.99 200 200 210 210 220 225 235 250 260 275 300 300 50 47 82 70 59 88 65 96 95 110 76 72 3.75 46.2 Oo63 3.78 44.3 o.63 3.75 44.8 0.62 3.93 47.0 0.62 4.49 * * 4.30 * * 5.10 * * 5.33 * * 5.86 * * 6037 11* Gaseous discharge Gaseous discharge 277 289 188 2l9 263 188 257 192 201 183 2.00 2.00 lo99 300 325 340 20 32 48 8.96 10.7 11.3 540 456 391 Vr 2 AV C K e texp 2 -it- * * * * * .. * * 40.6 1.24 * * *.,. ·~ 140 81 58 33 26 32 - 32 29 39 39 36 * Data not calculable on a ccount of lack of adequate resistance-temperature data. Vr/J seen from the results in Table XII which are summarized below. Metal D, mils w Ni Ni e, kcal/g.atorn Vo,volts 2.3 45-48 110-120 3.0 47.3 150 4.0 44 - 47 200-210 6.0 40.6 300 1.2 24-26 50-100 2.0 24.5 150 3.0 26.2 200 1.2 35.6 150 2.0 3406 250 3.0 33.3 250 Thus, roughly, to obtain the same state at texp, on increasing D by 1.6 mil we must increase Vo by about 50 volts. Since R is greater than 2.5 ohms for most of the experiments, we can calculate texp/R for these experiments without knowing R, the method being given in Appendix A3. The formulae for texp/R in terms of eq. 4 are complicated so that in order to see the consequences of eq. 4 on texp/R we examine the calculated values themselves. When texp/R is plotted against Vo linearity is not obtained, when plotted against log Vo satisfactory linearity is obtained, the slopes being of the order of magnitude of -1.9. Values o f ~ vgc have been R ~ plotted against Mon log-log paper (fig. 6). It is seen that the results for tungsten are considerably different than for the other metals. for W, tP.Yn ~ R vgc V- The results are; ..._ 58.1 M1 • 45 , and f 0 r N.l, 29 • 4 M1 • 08 •oo (7 ) ,,_ S,,00 fSo 3ooo ~ l'l-0 /30 2ooo V,,, volts JOO Effect of ViilY-~i"j 1 71 200,11 F ,o 3N t~H io V0 =2oovol-t5 70 8 &o ~'Rue ~ , P-Sec -.jou/§ ~ oh"" Zodo 3,1 ""'-ils c.orrer As+ -fi Ia...._e.'l\t.S Sl) /'W.X C11 A Fe 0 Ni O 'Pt Pf 0 'tc Ai'<" -so -1 atMOS' pit~ 2.0 IO 0 2. 3 W• i.o .1., CW\ 10 00 • i~i+~~J volf;je. S (Jl. 2.0 c.._) 11.D /10 Effect of vav-j i ~ M, /A· ~-a+o..,s/c"" If,- S" ' lo 1.0 .I A2-1 volts As o Au X Cu o Fe 0 Ni 1't J,cWI ! l 2. 3 4- + • ISO ff ec.ts of l~-~l\f- CYOSS~ ec.+,o....s- oh A1 ~+ Av X (00 C ~ P !i 0 0 Fis- ~ E 2.. Cvv Fe □ Nio "PtH w. .L a+o....:rJ .. VMI [ 14·3· c.,.._ 3 s lt For those experiments in which gaseous discharges occur, Vr/J = 26 to 39 volts/cm (with one exception of 50 volts/cm) compared to 2 to 156 volts/cm for the rest of the experiments in this section. These results are not surprising since a gaseous discharge might cease conducting under somewhat comparable conditions. The series of gold filament explosions are shown in plates 22 through 33. As Vo is increased, the vapor~like deposits on the slides become more readily observable. Also the hemispherical gold deposits observed at 632x decrease in size as Vo is increased. At 4.7x the deposit changes appearances with increasing Vo, more of the filament is deposited, cylinders about the filament axis appear, and the details on the cylinders become sharper. 1.98 cm gold filament, Vo~ 105 volts, e: 10 0 7 kcal/g.atom Plate 22. 4.7x Plate 23 Heavy splatter is seen at 4.7x. 632x The high power photographs, plates 23 and 24, have been taken in this region. The background has less vapor deposited than does plate 27 for which e : 26.1 kcal/g.atom. At the small e used, it is evident in plates 23 and 24 that the original filament shape has not been completely destroyed. Even at high magnification the background is devoid of metallic deposits. Plate 24. 632:x. An enlargment of plate 22. 2.00 cm gold filament, Vo :: 200 volts, e : 26.1 kca.1/g.atom Plate 25. 4.7x Plate 260 632x (This is another copy of plate 20 and of 21 included here for the sake of completeness of the present sequence.) The background is markedly different from the one in plates 22,23, and 24. 2.10 cm gold filament, v0 Plate 27. : 300 volts, e: (34 ) kcal/g.atom 4.7x On this plate Plate 28. 632x and on plates 29 and 32 (i.e. on all plates with still higher Vo), the complete filament pattern is imprinted on the slide. The balls in plate 28 are a little smaller than those of plate 26 (for which Vo was smaller). 2.00 cm gold filament, Vo: 325 volts, e Plate 29. 4.7x = (37 ) kcal/g.atom Plate 300 632x The appearance of this pattern is more uniform than the one on plate 27 for which e : (34) kcal/g.atom. However, parts of the two patterns are almost identical in appearance. The background in plate 28 is very shiny under high power when viewed under the microscope, whereas that background in plate 30 is duller. Plate 31. 632x. Part of background of plate 290 2 00 cm gold filament, Vo: 840 volts,~ 0 Plate 32. 4,7x D (46 } kcal/g.atom . Plate 33. 632x. The filament deposit appears to have several cylindrically symmetrical regions. The heavier deposits at the end may be due to the fact that the filament was clamped against the glass slide at its two ends. If we compare plates 24, 26, 28, 30, and 33, we see that there is a trend towards smaller ball starting with plate 26. In plate 24 the filament has not broken up int0 globules• at least not the protions deposited on the glass slides. c. Effects of varying filament length In this series of experiments, we kept Vo constant (200 volts) so that the initial condenser emergy was always A large range of filament lengths were used. 4.00 joules. When Vr is plotted against filament length a linear relation is obtained for intermediate filament lengths. For very short filament lengths, Vr is small on account of gaseous For very long filament lengths, Vr is zero dis charges. since there is not enough energy to blow out the filaments 0 The results for copper filaments are shown in fig. 6, the results for other filaments being similar. T:he linear relations may be expressed by equations of the form; Vr : G1J + G2 ••••••...•.......•.•••••.••• • {8) G1 and G2 are listed in Table XIII. If the data are examined (Table XIV) we see that we may assume that: K is independent of filament length for a given filament •• (9) Combining equations 1,8, and 9 and using the condition of these particular experiments, namely that V0 = 200 volts, we obtain, f E = w0 where = v8c/2 = G~c/2 • K + w1 Wo : • G1G2C w1 :: - af c/2 •••••••••••••. (10) These coefficients of powers of filament length are listed in Table XIII 0 TABLE XIII. Results for experiments in which filament length is varied for Vo ... 200 volts, C : 2OO~,and - L : 4 pJI for explosions in air at atmospheric pressure. Filamen!!,_ Metal D, mils w ,.. w xlO4 , K, o, .. Gt' Gz, w-1' vols volts joules joules joules Jou es cm cm cm2 Ag 3.0 2.60 167 O.37 o.94 o.O87 608 Au 2.9 6.4 181 0 0 24 o.48 o.231 41. Cu 3ol 4.5 156 0.61 o.95 0.140 20. Fe 3ol 1006 174 ... ( o.93 > o.369 1130 Ni 3.0 9.4 168 0 0 25 0.92 0.314 88. Pt 3.0 8.5 168 0.20 Oo97 o.2s6 72. w loO 2.0 198 000083 0.06 0.019 4.0 1 2.3 (10.8) (170) 0.13 (0 097) (O.367) (117.) 3.0 (30.5) (181) 0.26 (O.46) (1.10) ( 930.) 600 220 30 1.96 lv95 0.132 485. TABLE XIV. Results for moderate energy explosions in which j is varied for Vo : 200 volts, air at 1 atmosphere, 207., 4 ,Jili e Filament cm Metal D, mils Q, Vr, Ag o.89 1.40 2.02 3.35 45 164 162 159 3.81 1.32 1.39 1.48 o.4o o.73 2.00 3.07 4.98 15 176 169 161 149 3.98 o.9o 1.14 1.41 1.78 o.34 0.66 0.98 1.02 1.42 2.06 3.10 4.oo 4.47 5.28 23 45 62 64 150 146 142 137 135 136 3.94 3.80 3.62 3.59 1.75 1.87 1.98 2<112 2.18 2.15 0.91 1.30 1.60 1.95 2.39 2.97 3.32 45 67 145146 141 131 127 3.80 3.55 1.90 1.87 2.01 2.28 2.39 Gaseous discharge Gaseous dis charge lo2 1.98 100 3.00 Gaseous discharge 2.0 2.00 184 Oo61 (21} {0.066) :J.7 3.0 1.31 1.96 3.02 156 150 140 1.56 1.75 2.04 35.1 (26) 20.0 0.22 ( 0.24) 0.28 50 58 71 3.0 1.30 2.01 4.41 157 150 134 1.54 lo75 2.20 ·** ·** 48 58 80 Au Cu Fe Ni Pt 3.0 2.9 3.1 3.1 volts Av22 c, e, K, texp Vr/ , kcal joules~' volts/cm, for joules g.atom usec gaseous Ohm discharges. Gaseous discharge (36) 27.1 18.0 (0.38) o.37 0.36 Gaseous discharge (52) 26.l 2118 17.l (0.25) 0.23 0.23 0.29 * * * ** 21.5 (0.57) 0.52 0.60 0.67 0.67 0.64 * * * * * Oo20 38 (28) 34 44 60 Gaseous discharge Gaseous discharge Gaseous discharge Gaseous discharge (29) 23.4 15.6 12.7 11.s 10.0 51 (42) 45 49 68 68 63 63 (62) 66 73 80 83 81 49 52 64 63 70 85 91 50 TABLE XIV. (cont inue d } Vr Me tal D w 1.0 2.3 3.0 4.0 6.0 Av 2 c e K texp 2 Vr/~ 7r 6 2.00 2.70 4.00 194 192 190 0.23 o.31 o.39 o.47 1.94 2.60 2 .90 3.12 3.89 5.09 40 57 138 137 136 129 114 3.84 3.68 2.09 2.12 2.15 2.33 2.70 Gaseous discharge Gaseous discharge 0.98 1.50 2.06 2 0 50 2.65 2~70 2.91 3.21 3.27 59 66 106 104 103 101 94 76 82 3.65 3.56 2.87 2.92 2.94 2.98 3ol2 3.42 3.33 Gaseous discharge Gaseous discharge o.4o 0.80 0.90 o.99 1.08 1.13 1.20 1.40 1.50 1.60 1.68 1.79 1.so 1.90 2.00 2.60 39 60 69 77 65 69 80 60 65 55 65 65 40 50 47 0 3.85 3.64 3.64 3.41 3.58 3.52 3.36 3.64 3o50 3.7Q 3.58 3.58 3.84 3.75 3.78 0.13 0.39 0.71 1.00 14 22 15 0 3.98 3.95 3.98 * -'.i- * * 0.0083 43 ")'} * * 48.3 43.l * *- * * 49.3 49 0 2 47.0 * ** 0.12 0.13 {t- 4} ¾ * 0.26 0.21 0.26 8 10 75 76 77 88 112 * * * (50) 46.8 (50) 46.2 44.4 * * * * * * ** * * o.62 * 0.63 0.62 60 44 127 13 1 132 137 151 193 178 Gaseous discharge ** * * * * 85 29 98 241 241 191 225 213 183 241 225 258 225 225 32l, 277 289 No explosion. Gaseous discharge * 35.5 No explosion. * 1.96 108 442 517 * Data are not calculable on account of lack of adequabe resistance~temperature data. The net result of these experiments is that Eis simply related to filament length. very suggestive. This equation is If the minimum energy experiments are recalled, it was found that for filament longer than 0.7 cm, E c01 be . adequately represented b~ E :: Eo+E1.,,Q • In addition, E1 is negative for small diameters and w1 negative for a)-1 diameters. It is possible that the end effects of E for short filaments for minimum energy explosions could be taken care of without special treatment ·b y use of a term, E.l/J• Since K is practically independent of filament length for the present set of experiments, we have compared these values of K in Table XV with those obtained previously. The values of K for a given filament is the same for many cases. If we examine the values of w_ 1 we see that these are about equal to 0.95 joules for silver, platinum, copper, iron, and nickel filaments. w_ 1 /M for Furthermore the values of the tungsten filaments are 0.11, (0 0 35), (0.10), s.nd 0.10 for the 1.0, 2.3, 3.0, and 6.0 mil tungsten filaments respectively, and Ooll for the gold filament. Hence it appears that w_ 1 is a function of filament cross-section and is considerably different by a factor of about two for gold and tungsten and for the other metals studied. As may be seen in the following summary of the results of Table XIV, to obtain the same e as we increase D we must first increase filament length, then start decreasing it again. Filament Meta 1 D, iH!s Filament e,kcal/g.atom length ,cm Ni 2.00 21.1 3.02 20 0 0 4.oo 43 0 3 5.09 43.l 2.00 44.4 3.89 48.3 3 0 27 3.21 2.91 47o0 49.2 49 0 3 lo90 46 02 46.8 W 2.0 1.0 4.0 3.0 1.79 1068 lo8O {50) (50) We will now examine texp/R. Since the equations are very involved, instead of deriving the behavior of texp/R, we will use the calculated values to find its properties. It is seen in fig. 6 that t exp /R versus filament length is linear on log-log paper, this being true of all the filaments studied except tungsten for which the scatter is so large that no trends are obtainable. When gaseous discharges occur, we might expect that the gap potential at which conduction ceases is a function of gap length. For the uexperiments in which Vo was varied, Vr/t : 33 whereas for those of the present section in which filament length is varied, it is equal to 65. There is no obvious reason why the two groups of experiments should have different gap potentials at which conduction ceases. Therefore we calculated Vr/ Jl" to see if this function improved the agreement. We obtain; 1 for variable Vo, Vr/vf : 46 4 volts/cm2 for variable ) , Vr/i/J. 53 10 volts/cm2 1 : .••...•• (11) Thus for all the available experiments at atmospheric pressure, Vr/{f has about the same value for all the filaments. The series of gold filament explosions are shown in plates 34 through 45. The heavy metallic cylindrical deposits ·a re very wide for short filament length at 4.7x. Ball size as seen at 632x does not seem to be affected by gaseous discharge. The background de posit is considerably brighter for gaseous discharge. This may be caased by the heat of the discharge after the filament metal has been deposited. Ball size appears to increase, then to decrease as filament length is increased. A series of plates, 46 through 54, are given to show how typical filaments of the remainder of the metals for moderate energies look at 4.7x. These may also be compared with plate 55 for indium and plate 56 for gold leaf ( 632x) • o.40 cm gold filament, Vo: 200 volts, Vr: 15 volts, gaseous discharge. Plate 34. ,.7x Plate 35. 632x The deposit is very wide compared to the deposits on plates in the preceding section. At 632x the background 1s bright, the balls are small. Plate 36. 632x. An enlargement of plate 34. · This enlargement shows the intersection of three regions each with different characteristics. The colors of the background are different in each region as are the ball sizes. - o.73 cm gold filament, Vo .. 200 vol ts, Vr : 176 volts, e : (52) kcal/goatom Plate 37. 4.7x Plate 38. 632x The enlargment shows a typical group of spheres Comparison with plate 35 indicates that the balls are about the same size. Thus the sizes of the balls on plate 35 has not been affected much by the gaseous dis charge. 0 Plate 39. 632x. Enlargment of background in plate 37. This plate is very different from plate 36 as regards backgrounds. Plate 36 is very bright and smooth. may have been a results of the heating by the gaseous dis charge. This 2.00 cm gold filament, Vo~ 200 volts, Vr: 169 volts, e : 26.1 kcal/g.atom Plate 40. Plate 41. This is a duplicate of plate 20. 632x. The differences between this plate and plate 37 are numerous. Since e for plate 37 is two times as large as e for plate 40, this is not surprising. The main differences are the width of the cylinders, the characteristic details of the cylinders, and the heavy black deposit on plate 40 0 The balls in the enlargment are considerably larger than on plates 35 and 38. 3.07 cm gold filament, Vo: 200 volts, Vr: 161 volts, e : 21.6 kcal/g.atom Plate 42. 4.7x Plate 43. 632x Not much metal has been deposited on the slide. Very few balls were found.. These balls are smaller than those on plate 41 and larger than those on plate 4.98 cm gold filament, Vo= 200 volts, Vr s 149 volts.,, e : 17.1 kcal/g.atom Plate 44 4.7x Plate 45 632x Only a portion of the scant metallic deposit has been photographed. Plate 46. 4.7x Tungsten 4.0 mil filament Air at 1 atmosphere Length = 1 o 96 cm The condenser was charged to 150 volts and discharged through the filament without blowing i t out. A second surge with Vo: 300 volts blew it out. A gaseous discharge occured. The large white cloud has a bluish tinge. Plate 47. 4.7x Tungsten 4.0 mil filament Air at 1 atmosphere Length= 2.00 cm A single surge with Vo• 275 volts blew out the filament. Unlike plate 46 there is only a small amount of cloud. Plate 48 4.7x Tungsten 1.0 mil filament Air at 1 atmosphere Filament length: 2o00 cm Single surge, Vo : 100 volts Vr:: 89 volts There is a distinct blue cylindrical film on this slide that is more like plate 46 than 47. Plate 49 4.7x Nickel 3.0 mil filament Air at 1 atmosphere Filament length : 2 00 cm 0 V 0 -• 300 volts Wr = 51 volts Gaseous discharge 0 Plate 50 4.7x Platinum 3.0 mil filament Air at 1 atmosphere F'ilament length :: 1.90 cm Vo • 225 volts Vr = 63 volts Gaseous discharge Plate 51 4.7x Copper 3.1 mil filament Air at 1 atmosphere Filament length : 2.00 cm .- 200 volts Vr - 146 volts Vo e : 23.6 kcal/g.atom Plate 52 4.7x Silver 3.0 mil filament Air at l atmosphere Filament length: 1.40cm Vo : 200 volts Vr: 164 volts Plate 53 4.7x Iron 3 .1 mil f ila.ment Air at 1 atmosphere Filament length • 1.97 cm Vo Vr - 275 volts -- 74 volts Gaseous discharge Plate 54 4.7x Cqnstantan 3.1 mil filament Air at 1 atmosphere Filament length~ 2.48 cm Vo : 275 volts Vr • 220 volts We will now examine the constants for the moderate energy explosions relations. At Vo= 200 volts and filament length equal to 2.00 cm, the residual voltages in equations 4 and 8 are equal. Thus we obtain, = A1 ( 200 - A2 ) •••••••••••••••(12) This equation is used to calculate A1 for comparison with A1 obtained directly from the experimental data (cf. Table XV)• As is obvious, the comparison for tungsten is poor. Since it has been assumed that K is constant for both series of experiments, the average K for each set is listed in Table XV along with K for minimum energy explosions for both the graphical and analytical values. It is apparent that these average values of K are about the same for experiments carried out under a wide range of conditions for a given filament. In a sense this result is reassuring since, if the average values of Kare about the same, smaller changes in conditions caused by changing Vo or filament length should not have more pronounced effects on K. TABLE x:J. The energy dissipated in the apparatus, K, is compared for a variety of conditions. In addition the constant A1 obtained from the experimental data by means of ego 4 is compared with A1 obtained from eq. 12. Agreement between these two values is a test of consistency of the variable initial voltage experiments with the variable filament length experiments at moderate energies. Filament Metal D, mils K, joules Moderate en~rgy Minimum explosions energy Vo ]l explosions varied varied graph•ana!ical ytical Ag Au 0.21 0.24 Cu Fe 0.13 Ni 00013 0.061 {0.04) 0.13 - 1 0 34 - {0.03) 0.014 1.10 • 0.066 0.061 0.050 1.15 0 0.25 Pt .. w 3.0 o.oos3 o.os5 0.13 (o.oos4) o 0.1s o.os 0.24 o.41 0.26 - 1.48 4.0 - 0.19 3. Study of chemical reactions of Electrically Exploded Filaments with a number of gases. Initial experi~ntis indicated that exploded copper A number of other filaments reacted strongly with ammonia. gases were then tested at pressures less than 100 mm, namely, There was no reaction of the exploded copper filaments with any of these gases within experimental error which was rather large since a meter stick was used to take readings. In these experiments C: 50 f-F, Vo: about 270 volts, but rand Lare unknown. The reaction was followed for 24 hours. An upper limit to the amount of gas that might have disappeared would be at most 0,2 mole of gas per mole of copper filament. The reactions with ammonia were re-investigated with refined apparatus. C: 200 A cathetometer was now used. With p and L: 4 Jill, a 3.0 mil gold filament 1.90 cm long was placed in an ammonia atmosphere at 82 5 mm pressure. 0 It took four days before the pressure became constant at 82.5 mm pressure. Apparently the brass in the apparatus reacted with or adsorbed the ammonia. (VO: 200 volts, Vr = 48 volts) After the explosion there was no change in pressure for 19 hours. A 3ol mil, 2.00 cm copper filament was exploded in an am~onia atmosphere. Three days were required for the system to attain a constant pressure of 81.1 mm. After the explosion (Vo: 200 volts, Vr: 142 volts) no observable change in pressure was noted in 24 hours. An upper limit to the amount of gas that might have disappeared would be at most 0,02 moles of gas per mole of copper filamento 4. Experiments with indium filaments Indium filaments were prepared by drawing out a glass tube, with an indium metal pellet inside, in an oxygen:' gas flame. The glass Wijs removed in hydrofluoric acid. Uniformity of the filaments was poor. In plate 44 is seen a typical slide at 4.7x of an explosion of an indium filament. The results for indium are given below; Vo : 2 00 v o 1 ts , C = 2 00 fF , L : 4 /lli- , Air at atmospheric pressure, j D, mils Vr, volts 3.2 72 3.7 66 4.0 ?l 4.8 125 5.3 68 5.7 123 6.1 120 7o3 99 s.3 22 9.7 59 = 1.98 to 2.98 cm. Plate 55 4.7x Indium 4.0 mil filament Air at 1 atmosphere Filament length: 1.98 cm Vo : 200 volts Vr: 71 volts Plate 56 632x Gold leaf 2.8 cm long 1.9 cm wide Air at 1 atmosphere Vo -- 200 volts Vr = 176 volts 5. An explosion using gold leaf. An explosion with gold leaf is shown in plate 56 at 632x. It is of interest mainly to show that the features found on the slides for gold filaments are characteristic both of the gold and of the filament shape. The gold leaf pattern is unlike that of any of the gold filaments. E. Summary and conclusions The study of the low voltage electrically exploded wire was undertaken to see if it could be used as a source of metal vapor. Finding that filaments did not vaporize as expected, we studied the nature of the processes occuring by determining the amount of energy dissipated in the filaments and by collecting the metal onr~ gla.ss slide for microscopic inspection to ascertain the nature of the exploded metal. It was found experimentally that for minimum energy explosions in which filament length was varied the total energy dissipated, i.e. the energy lost by the condenser, was directly proportional to the filament length. From this fact we were able to obtain the total energy dissipated in the filaments per cm. The temperatures corresponding to these filament energies decrease as filament diameter is increasedo The average filament temperature decreases a little as filament length is increased for small diameter filaments. There appears to be an effect due to changing capacity and inductance, but this has not been established quantitatively. When helium is substituted for air at atmospheric pressure the minimum energy explosions seem to be unaffected. In order to test the hypothesis that the filaments blow out on account of vaporization, we have examined the glass slides on which the exploded metal is deposited. As yet no metallic deposit have been found that would indicate that vapor was present with minimum energy explosions. TABLE XVI. Summary of Voltage Relations found Experimentally. 1. Minimum energy explosions 2 0 Moderate energy explosions a 0 Variable pressure (gold, 2.0 cm, 3.1 mils) 4.00 joules available 10- 4 to 135 mm Av 2 c : 3.66 to 3.97 joules 50 to 760 mm Av 2 c b. Variable V 0 2 2 Vr ~ A1 ( Vo A1 c. Variable ~ : 1.14 to 1.57 joules • << A2 Vr: o1 }-t--o , 2 f 0 1J 0 2 «: A2 1, TABLE XVII. Summary of the Effects of the Variables Studied on E. 1. Minimum energy explosions Filament length cl> o.7 cm) E : E 0 +-E 1 2 J , where I E11«,E 0 Filament diameter d(E/D )/dD < O, so the explosion temperatmre (average) decreases with increasing D. Filament metal Eis strongly dependent on the filament metal. Gas Eis the same in air and in helium for nickel. C and L There appears to be an effect. 2, Moderate energy explosions a. Variable pressure for 2.0 cm 3.1 mil gold. 4.00 joules available. b. Variable Vo E: 0.46 to 0.62 joules/cm, 4-18 %vaporized at explosion, for 50 to 760 mm. E: 1.60 to 1.76 joules/cm, 85 to 100% vaporized at explGsion, for 10-4 to 1:35 mm. • 2!" ~a.se.o us c:l.;s cL, .._v-JC2.S oc,v ..... '2. i E =~ z 1 VO • For I( ::. constant, the z 1 are directly ootainable from tne equations in Table XVI. 0 Diameter To obtain the same state at explosion, on increasing D by 1.0 mil, Vo must be increased by about 50 volts. Metal Eis strongly dependent on the filament metal. c. Variable J Diameter Metal .... "1 E : i.:v 1 X • For K = constant, the wi are directly obtainable from tlle equations in Table XVI. To obtain the same state at explosion, on increasing DJ--i0 must first be increased then decreased. Eis strongly depefkl.ent on the metal. f ila.ment A series of vacuum explosions were carried out at moderate energies. It was found that from 50 to 760 mm the explosions were unaffected by changes in pressure from the standpoint of the energy dissipated in the filaments. However the mean size of metal globules deposited on the glass slides decreases with lowering of pressure. •A A different process occurs from 10 -x to 135 mm. One or the other of the two processes occurs in the pressure range from 50 to 135 mm. This second type of process is characterized by a much larger total energy dissipation and decrease in size of metal globule on the glass slideso At 10-4 to I mm the metal deposits appear to have been largely of vapor origin. The states of the filaments corresponding to the high vacuum results are ambiguous. Further data is need to determine whether the above processes are due to gas discharges or to the calculated states at time of rupture of 85 to 100% vaporizedo Two further series of moderate energy explosions were carried out at atmospheric pressure. In one series, the initial condenser voltage was varied, all the other initial conditions being reproduced as closely as possible. It was found that the residual condenser voltage was proportional to the initial condenser voltage. This result implies that the energy dissipated in the filaments is a simple function of the initial voltage 0 At higher energies than the minimum explosion energies, the assumption that the energy dissipated in the apparatus for a given filament is a constant leads to an error of less than about 5%. On using this assumption we are able to determine the total energy dissipated in the -41• filament per cm directly from the experimental results without need of such data as resistivities, heat capacities, etc. In a second series of experiments, the initial voltage was kept constant and the filament length was varied. Here it was found the the residual condenser voltage was propDrtional to the filament length. Using the same assumption as for the variable initial voltages, we arrive at corresponding results, namely that we may determine the total energy dissipated in the filament per cm directly from the experimental results with only initial conditions specified. As an example of the significance of these results, suppose we have a metal filament into which we wish to introduce a given amount of energy. By performing a series of minimum energy explesions and a series of moderate energy explosions we will be in a positiom to specify the initial needed to give us the desired result. A series of experiments have been carried out to see whether any changes in pressures result from exploding filaments in a number of different gases. in our experiments 0 We obtained negative results Appendix A. Derivations In this section we shall present the derivations of the principal equations used in this paper. In all this work we assume that C and Lare constant during the surge. In addition we assume that the principal energy effects of the electrical surges are the Joule heat dissipation, phase changes in the filament metal, and skin effects in the apparatus. Radiation losses, heat conduction losses, the Thomson effect, and the Peltier effect amount to less than o.03 joules under the most extreme conditions encountered for times less than 400 microseconds. been neglected in all cases. These effects have There was a maximum condenser lag of 4 volts which has been neglected even though it may be of importance in some cases. The derivations are restricted to explosions in which gaseous discharges do not occur since Joule's Law is not applicable to these dis charges. 1. Derivation of Equation 1 0 The energy dissipated in the region of filament x to x -t-dx at time t to t +dt is equal to f°(~,t) 12 dx dt. The total energy dissipated in the filament is equal to E) : f ! Jx:O Jtexp i 2 ;O(x, t) dt dx t:O / =Jx-o ri l+oo 12 ((x,t) dt dx t .... - - : IJ i 0o ,_,(x) dx• X:0 £+ From Joule's Law. 1 : 0 outside of t:O to texpo 00 t:: -oo 12 dt By definition. The total energy dissipated in the apparatus (excluding the filament) is equal to texp 12 r dt : r" t:0 ~ r;: _. , 2 1 dt The total energy dissipated is therefore given by, Av 2 c 2 If = ER+ r E.,f f;:i(x) dx f....... (x) :. -:; 1 (j) which is i!l.dependent of x, then \ - E [1+ f] • Thus the simplest derivation of eq. 1 is that in which it is assumed that the filament resistance is uniform at any time t. If f(x) is not independent of x the situation is more We will make a few simple assumptions to complicated. see what happens. Let us assume that the filament blows out for minimum energy explosions because of vaporization of hot points. We now replace tbe term, j---- (x), by two terms, one for the hot points (h) and the other for the main portion of the wire (m). Let f be the fraction of the wire occupied by the hot points. i ~ f' (x) dx [ tX:0 \ Then r.1.rh and -... If the number of hot points is distributed frem the macroscopie: viewpoint uniformly along the filament so that f is independent of filament length, then the above equation may be in agreement with eqo lo 2. Current The system is a circuit in which an inductance, a capacitance, and a resistance are in series. To avoid mathematical complexity, we assume that Risa constant during the surge. Our system is always overdamped so that . . . . . . . . . .- . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 13 ) . The well known solution to the above is; i - -at Vo mL where a : e sinh mt •••• 0 ••••••••••••• ( R ~ and m :/ a2 .. 14) 1 LC :Z0 Time at which the Explosion Occur:-s The total energy dissipated is equal to r texp i 2 t.o which is integrable for constant R if we use eq. 1 4 . R dt, After integrat i on we neglect two terms which are negligible compared to the terms retained in almost all cases. For example for some of the copper filaments the values of these Solving for texp we obtain, - texp \ For R )2.5 ohms this reduces texp/R = 2.303 Clog Vo/vr to •••••••••••••••••••••• (16 ) 4. Effect of Variat i on of E and F with Filament Length on E{graphical) for Minimum Energy Explosions. We will assume that E by E: E 0 +E1j and F and F may be adequately represented = F 0 ~F 1 f o We have by definition, .ti. 2 E{graphical): d v c 2 a t o Combining these with eq. 1, we obta.in for the amount of energy dissipated in the filament, e = e(graphical) 1rF1 +-<l 1-FJe1/e ••.......................... ( l 7) If we assume that the analytical results are satisfactory we may re-write this as, ( ) +- F) el e(analytical) e{graphical) e(s.nalytical) 50 ••••••• 0 • { 18) Mean Filament Resistance Hypothesis and Skin Effect Corrections When ~ v2 c/2 was plotted against filament length for minimum energy explosions a straight line fit was found to be valid within experimental error. The reliability of the numerical values of the constants defining these lines was adequate to enable us to interpret the results. Since these straight lines were obtained it appears that the assumption that E and Fare fairly constant for minimum energy explosions appears to work. However the numerical values of F {which is equal tor/ (' ) are incompatible with the use of the direct current resistance for r. If the direct current apparatus resistance is used, values of f' (obtained as r ;F ) are found to correspond to 300 to 500°K instead of reasonable values of the order of 1000°K for copper, silver, and gold. Another example of this difficulty is furnished by the constantan data. Constantan fil a rrents were used for exploratory experiments. For 200 pF and . 1 J1H, F : 0 56 cm. 0 Since the resistance of constantan 3.1 mil wire is 1.0 ohms/cm from room temperature to the melting point, it is probable is of the order of 1.0 ohm/cm. that -r - Therefore, -- 0.56 ohms, which is about 5 times as large as the direct current apparatus resistance. Since the values of p are needed to make skin effect corrections, it is necessary to assign reasonable values to ( in order• to obtain ft-• It is assumed that (' is equal to the filament resistance ~hen E/2 joules have been dissipated in one cm of filament. When the state of the filament corresponding to E/2 is that of a partially me 1 ted solid then (° is obtained by assuming that the 1 iquid and solid are distributed uniformly along the .filament. When the state corresponding to E/2 is that of a partially vaporized liquid, then is obtained by assuming that this resistance is equal to the resistance of the unvaporized liquid at that temperature. The use of kkin effect corrections is reasonable since the rate of change of current is rapid during a surge and since there are several conductors in the apparatus with relatively large cross-sections. These include switch blades, coaxial cable, brass standard taper joint, and soldered joints. The filament diameters are too small to have pronounced skin effect corrections. that the apparatus resistance r We assume is proportional to the square root of the frequency and the effective frequency is inversely proportional to the time at which the current attains its maximum value. The curve in fig. 7 is drawn to satisfy the above as well as to pass through the point for copper. Tk poi ...--t-s ,1~ oJrt;ai~ li,.!J assu...._i ".j ~at- R~2.oc-.. a..J.. ,,_.,,, Ftjr~r4·.c.at),,t5C-fJ. °TIie has /.ec....._ cv'C"VC. J.,.. ,.n., f:o pas: s ~"'" o uj 4 f:...- f;J..c. roi>1i- + Ni 3,0 11ti /s l\f," S:o CQrreT' tJ..,f A.Q(Vf"t"EtUf'>IC_:,. c-2o~F L:: "/H Au Cu ,o 1, oh,-,,, ~ +Ni £o'l'Ylils /.0 /0 ~ 11 7 6 5" .,. Lo3 ~ 1/'0'. I Oj f (a.,;al~t-ic.al) for L.7 J {a.-u/7/,,o/) Y> - Lo7!3 fo,_,/:i•e&IJ (. • .,,.. 7n,,.,, "1 v '-' a.,,., ~,,.'J~ tni"'i""v"" axf/o:,1on . / d/..,.os/°~~Y'(Z - - A!I 3 .0 m,I. 1.00 - - c,._ 3 .1 m, ls - A u 2 -'f md, c,y.f'/osio11s. f'rOI,>\ A.l!o.-.7. 4.A is de.,;,...,_~~J as 1c., ( 4:f" )IF -4 / ' H 2.. eYteY-j~ ~ is obt~it'led i"' +"-ct "t:.c.11,i:.) I.Jo' - - N, s:o rn,1, 1.2. totils •2. - Ir/ 4.oM,/, - 1,,/ 4J:!:'. 61' ff,• oh"'s C.'°'\ Ni 3 ,o..,:ls J .O -,,,,/, - - Pl J . O tn,/, W 4 -0 m,/, o--Ni +.o.., :1s Ni s.o,..ils .3 - F e J./ rn, f, Au 2 ,9 ,.. ils /(i 7.0 ,,, , /, W .l.3 ....,J, /l'i ;i (ana/. {,ca/) o/n,.,, ' C.,.., ~-";-I----=11=-z--:,-o,'::;-3----::o,7."'f--O::.l,~~0.,~ .7-!,i:-c!f~IJ_ ,o_ _ _..J2_ _3l.___J_i/-_JLJLJ--1...lJ Fil 7 2.~ .... ,• Ni 2,0 --.:Is F• 1 . 1 "-'ils W -Yro""":ts, 'Pt" 3 ,0 ...,;Is p, ohms Appendix .B. Relations between Mean Filament Resistance and Effective Apparatus Resistance for Minimum Energy Explosions. We have been using fig. 7 to evaluate r. If this curve is replotted on log-log paper it is found that the relationship becomes almost linear. We wished to see how r( analyt ica.l) was re lated to f=>( a.nalyt ical). The \ situation is too complicated mathematically to derive the relation directly so we have examine the analytical results themselves. The linearit"IT " of r versus p- -~() on log,.;.lcg paper was suggestive, so we plotted b:0th r(analytical) and r 1 against p(analytical) on log-log I paper. It is seen in fig. 7 that satisfa ctory linearity is obtained. 0 .27 ohms. The value of r 0 has been assumed to be Appendix c. A possible Source of the Large Mean Deviations in Explosion Times. The mean deviations in texp/R is about 20% whereas that in e is about 4%. ·Most of the scatter in the former may be accounted for if we assume that the scatter in e is due to the possibility that a gi~en filament may blow out anywhere in the energy range, e - 4% toe +4%, and not restricted to the given e). An order cf magnitude calculation with the copper results yields the result that the scatter in texp/R,due to indeterminancy in e of 4%, is 11 to 22% which is of the same order of magnitude a.s the value of 14% for copper. For small Vr the corresponding mean deviation int exp becomes very large. On account of the logarithmic nature of the functions involved, the values of texp corresponding to e +4% may become very large or infinite or imaginary (which simply means that the filament does not explode) whereas the values fore - 4% will be only a little smaller than those for eo Thlis is one possible reason why we find some very large texp/R in Table IV but no excessively small ones. Appendix D. Minimum Energy Explosions with Constantan Filaments for a Number of Different Circuit Constants In most of the exploratory experiments for minimum energy explosions, constantan filaments were used to test the behavior of the system. This exploratory data is not as closely controlled as the data for the other metals. In addition to this, when much of the early work was done, a high resistance voltmeter had not yet been built so that in some of the calculations we have had to neglect Vr. In the results summarized beiow, the possibilitI appears that the inductance affects Emore than does the capacity. A series of experiments to examine this more fully would be interesting. Minimum energy explosions of 3.1 mil constanta.n filaments in air. Type of lead to filament contact. E (graphical), joules F, cm pH 50 l Monel capillary 0.268 o.39 200 (1) Monel capillary Oo255 0.56 Capacity, Inductance, fF ExEei'iments for which Vr has been omitted. 50 l Gold capillary 0.242 0.69 50 l Solder 0.240 o.s4 50 11 Solder o.275 0.29 Appendix E. Bibliography - Anderson: Proc. Nat. Acad. of Sci~ , 6, 42 (1920); 8, 231 (1922 ) - """ Anderson: Astrophysical Journal, 51, 37 (1920) -- - Anderson and Smith: ibid., 64, 295 (1926 ) Decbene: J. de Phys. et la. Rad., 1, 59 ( 1926) Eckstein and Freeman: z. Phys., g!, 547 (1930) - Fuku.nda: Inst. Phys. Chem. Res. Tokio Sci. Papers, 6, 1 (1927) Futagami: ibid., ....__ 31, 1 (1937) Hori: ibid., .,.,. 4, 59 (1926) Menzies: Proc. Roy. Soc. London, A 117, 88 (1927) -~ Nagaoka and Futagami: Imp. Acad. Tokio Pree., _g, 254,387 ( 1926'); 3, 499, 643,1927); 4, 106, 201 (1928); 11, 43, 171 (1935} """ - - """ Na.gaoka and Futagami: Inst. Phys. Chem Res. Tokio Sc 1. Papers, 8, 269 (1928); 25, 111 (1934} - Nagaoka., Futagami, and Machida: Ibid.,~, 169 (1932) Nagaoka, Futagami, and Machida: Imp. Acad. Tokio Proc . , ,g_, 328 (1926); !, 195, 198 (1928) Nagaoka, Nukiyama, and Futagami: ibid.,~, 208, 212, 258, 262, 319, 324, 331, 392, 398, 403, 409, 415 (1927) - Nipher: Proc. Amer. Phil. Soc., 52, 283 {1913) Nipher: Experimental Studies in Electricity and Magnetism. Bla.kiston , 1914 Rosen: Bulo Soc. Roy. Sci. Liege, 405 (1941 ) Rosen : ibido, 176 (1944) -- Rosen: Nature, 156, 570 (1945 ) Sawyer and Becker: Astrophysical Journal, U, 98 (1923} - Singer: Philosophical Magazine, 46, 161 (1815) Singer and Crosse: ibid., 46, .......... 259 (1815 ) Smith: Proc. Nat. Acad. of Sci., 10, ...,._ 4 (1924) - Smith: Astrophysical Journal, 61, 186 (1925) Sponer: Die Naturwissenschaft, 12, 619 (1924 ) Suyehiro and Nagaoka, Nagaoka Anniversary Volume 23 (1925 ) Vaudet: Compt. Rend., 198, ...,.,.... 1217 ( 1934 ) We ndt and Irion! .T _ Am_ f'!h al't'I <::!,". • 4___4 _ --1B8.7 ( 1__9_22._l Propositions Submitted by Sam iJaidi tch Ph.D. Oral Examination: April 25, 1947; 9 :00 A.M., Crellin Coni'en:nc e ?:c.·Jm Professors Yost (Chairman), 3a.dger, Epstein, liuce.s, liiemann, Pickering, Schomaker, Sv1ift, and Dr. Davidson Inorganic Chemistr~ 1 1. Gomberg state,a t.}1.at he has obtained perchlorate free radical, 0104 • alternative hypothesis is more reasonable on the basis of his facts, namely, the format ion of IC104 • 1 Gomberg: ~• .J\m. Chem. Joe.,~, 398 (1923). 2. An A scheme for classific~~ion of boron compounds is sugge$te4: I II Ca.Bs B2Hs Ca.Be B4H10 t/ig3B2 :BsH9 III K~2~(0H)2 IV V Ni~ . Hs:l30s :BC1 3 Chemical Kinetics 3. Fundamental contributions to our unde:rstanding of chemical kinetics might result from thorough investigations of kinetics in the liquid ammonia,...sodium system. Since one of the reactants in such studies Yrould be a particle in a box (electron or electron pair in a hole), it i s possible that the interpretation of expe rimental rosults could be carried out more satisfactorily than in the c a se in ordinary solutions. The situation is in some vmys similar to electron scattering experiments. 4. Kinetic studies of the reaction of deuterium nith :B2-B: 6 might yield positive information regarding the structure of diborane. 5. The data of Burg and Schlesineer for the decomposition of BH~CO are incompa,tible viith some simpl e mechanisms involving (BH 3 ) 2 CO as an intermediary. The authors are correct in assumin6 that the data can be accounted for by assuming :BH 3 as an intermediary, although they have not pr oved that this is so. 1 Burg and Schlesinger: i· _.'\m. Chem. Soc., 730 (1937). 1 zz, Low ancl Hit;h Pressures 8.nd Temperatures 6. proposed 1 Unlike the method described by Strong, the procedure/\belor: doe s not require evaporation of the aluminum as soon as a non-conductin6 vacuum has been reached. Heat the glass (in vacuum), then vaporize enough aluminum to form a thin non-opaque film. Allon the glass to cool. Then dr3pcsit aluminum until the desired thickness is obtained. The operations are a rranged in such a manner as to reduce the number of pin-holes, avoid bl 'Jorn, a::1C:L increase adhesion and hardness of the aluminum f:i:.lm. 1 strong et al: Procedures in Experimental Physics, Prentice-Eal1, Inc •• 1941, p. i'f6. 7. In certain industries fluorescent materials have been developed for many uses. Since these materials are norr available commercially, it seems reasonable to use them for laboratory practice. The :following is suggested as a method to detect vacuum leaks: First, immerse the unit vith the leak in a fluorescent penetrant. Then drain, wash with cold uater to remove excess penet rant , and dry \"Ti th a rrarm air current. Next, apply developing powder. This draws out the penetrant, thereby magnifying cracks. T'.nen inspect the unit under black light. 8. kn experimental study of the sodium-ammonia system at moderate pressures would be of great value. The minimum result might be the solution of the current dispute as to whether the solid system is a super ... conductor. Optical as i!ell as electrical properties should be closely observed since a sudden transition may occur if Ogg 1 s theory of electrons trapped in holes is correct. 9. Tungsten rney not have a critical point, that is, it mey not b~ possible to go from the liquid to the vapor state TTithout going through an intermediate state in ,:,hich there is a boundary between tr10 phases. This question could be investigated by means of the high energy electrically exploded Thermochemistry wire. 10. A re-assignment of the values of the heats of formation for BC1 3 a~d BBr 3 is proposed. In addition TTe may assign a set of tentative numerical values for the heats and free energies of formation of B4 H • 10 B5 H11 , B2 H5 01 and B2 H5 Br. 11. The first and second acid ionization constants of potassium hydroxylamine disulfonate may not differ from each other by more than a factor of three. Aesthetics the basis of the experiments of TTeber1 , a. theory of change in taste in art and a theory of the differences in taste betr,een the artist and the public can be proposed. A series of ne,-, experiments mey be suggested to test these theories. !,.7eber: ,;r. ~EE1-ie9; P§lch., J:2, 310 (1931). 12b. ':Lhe philosophical foundations of a satisfactory theory of modern art have much common ground to those of modern science. 12a. On -3Chess -· 13. A knight sacrifice gives ,;ihite a lively nttacl:: aeainst Tarra.sch' s1refutation of the Heti attack. 'That is: 1 1. 1T - IG33 p - Q4 2. ? - l34 p - Q5 3. P - QH4 P - IG33 4. P - K3 P - K4 5. :i:T x KP Tarrasch: l'1J.1e Game of Chess. 1 Lic:(ay, 1935, P• 407.