I i III” § H‘ § ‘ , \ — \< — ‘ — ‘f x — — \V E — ¥__ _:_ — , ~ _. -§ \ — I 116 336 HTHS THE EFFICIENCY OF THERMOELECTRIC GENERATORS Thesis I'M Hm Degree of M. S. MICHIGAN STATE COLLEGE Richarfi ‘WéIIiam Lawrie "I949 W's ' VIII ”TIIN'VIRI'TL'BIWI 321293 01093 9092 This is In cerliIlJ that the? thesis cntitImI The Efficiency of Thermoelectric Generators prescnlm] In] Richard Laurie has Inc-en acrelplwd Inwards IulIiIlmcnl M the requirements Inf 7 “.030 dvgrmi‘ in EoEo .‘Iflinl‘ III'U hate Kay ,5,_ 1.94:9 M-Tt'fi PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE Mam»- 1/98 CJ'CIRCxDateDue p65-p 14 mt- -. I.’ IE EFF ICIEXCY 0F TLZRIOELaoTnIL }T"E”1TOP BY Richard William Lowrie u. Submitted to the School of Graduate Studies of Michigan State College of M rio ulture and Applied Science in partial fulfillment of the requirements for the degree of Department of Electrical Engineering 1949 IHESIS 'T" -“ 'T T_" {\fi r1 xx ‘31“ 17‘ “1’71 Ix -hkA— 51 V— V\~~-L.4-I.LA m litle Intro ucticn Encr"y Con'ersions EXperimental Investigations n of a Small Generator Kathenatical Analysis Efficiency Analysis Tables and Graphs Thermoelectric Constants firanhs Bibliography 7‘ 4i p.- m} G. 6““ w r 5‘s w IU U1 0‘ O\ \O -1,_ Introduction Thermocouples provide a means for converting heat energy directly to electrical energy. There are very few other phenomena which accomplish this. The potential usefulness and scope of application of thermocouples is great since the energy conversion is direct, no rotating or moving parts being necessary. However, the efficiency is at present very low , and this limits the applications of thermocouples to heat measurment. p .esearch on the phenomena of the thermoelectric effects is now being pursued in various laboratories. Most of this work is experimental in nature, consisting of investigations into the physical properties of semi- conductors. There is no satisfactory theory as yet to explain all the fee ures of thermoelectricity. When the theory is complete; then the proper materials can be immediately selected which will give the optimum efficiency to a thermoelectric generator. In lieu of a complete theory, the method of approach “as been to use the known facts as a guide to extensive experimental investigations. Energy Conversions Of the various types of energy or sources or power, the following must be included: heat, or radiation in general; mechanical, electrical, chemical, potential, and nuclear energy. Each of these sources of power have certain characterestics which limit their range of use- fulness. This ran: e is not entirely ir herent in the nature of the energy, but may be ex Mp nded in many cases by new applications. For example, one would not expect to drive an ocean liner on its trip by the use of the electrical energy stored in a larg e condenser. Such a condenser would be enormous by present standards. Yet someday such sources of power may be commonplace, if research discloses a material with suitable properties. Such a material might be one like barium titan ate, which (1) this could has a dielectric constant of 11,000. be increased by a factor of 30, and if the dielectric strength could be increased by a factor of 20 and the resistivity by a factor of 100 then 100 kilowatt hours of electrical energy could be stored in a volume (2) of 2 cubic feet for several weeks. 0f the above listed forms of ener3y, the most versatile is electricity. Large amounts of electric 6 #19 %31 #33 'd cwer can be transmitted with small loss over long dis— tances by small wires. The advantages of electricity to the production of motion are too well known to be men- tioned. Electricity can be converted into heat with per- fect efficiency . The desirability of having a large sup- ply of electricity available is obvious. The best way to obtain the electricity is not, however, so obvious in every instance. If, near the user of electricity is a large waterfall or swift river, the economics of the sit- uation immediately direct the consumer to the cheapest source, a hydro-electric plant or a steam turbine-alter— nator plant. If the consumer is only going to use n F.) T"Jt! average of 500 he“ a day, a diesel plant might be more economical. If the consumer is a farmer, isolated from a public utility power line, he may use a gasoline unit or a wind menerator, or batteries. These are the main La sources of electricity in use today. Others are be- ing developed, however, such as tides, geysers, solar heat, nuclear heat of reaction, and various electrochem- ical reactions including photosynthesis. The nuclear pile as a source of heat energy has been considered for several years, and experimental ’3 units are now being tested. T The advantages are that there is a very low fuel cost and a very slow rate of I‘D LU _ .1) he he —\]r0 V\J :0 - {D I .. 3%: ”ti: fuel usage. The radiations mak necessary heavy shield— l 5, however. Magnetostriction :enerators have been studied as a possible source of electricity. The efficiency is good, but very little research has been carried out on this (1) method to determine the advantages or disadvantages. The usual process suggested is to change the length of an iron bar by mechanical means or heat, and then util- k) ize the corresponding ch=n e in magnetic properties to I V S produce a volta e. Another Similar idea, proposed by Edison, is the thermomagnetic generator in which the change in the permeability of an iron bar in a magnetic field, due to rapid heating and cooling, changes the flux linkages in a surrounding coil.(2) Edison believed the efficiency could be pushed up to a reasonably high value, but he realized that such a jenerator would necessarily be relatively heavy. a device for generating electricity from light by means of selenium cells has been described in the liter- ature.(3 ) Due to the high resistance of selenium, how- ever, little current could be obtained. Considerable work has been done on utilizing the rise and fall of water due to tides, and some work has (1) RCf. # 5,1; 10 (2) Ref. #123 (3) Ref. ,“116 U1 been done on harnessin the iorce of the waves.(l) U i find ienorato s 1 small sizes are in wide use on \— ’“5 CS farms and on aircraft. Large units are not widely used due to the fact that there are very few locations with a strong wind available. Various means have been suggested for converting chemical energy to electrical energy.(2) Storage batter- ies are heavy and bulky. A storage battery which could efficiently store, 100 times as much energy as is now possible, could be very widely used in every place where electric power is utilized. About 1898, a great deal of discussion we given to the production of electricity from carbon in a carbon-metal heated cell.(3) At that time, an overall efficiency of ,4} was thought to be quite eas- ily attained, and some units were built which looked prom- ising. It was eventually decided that such a method would not be commercially feasible, and the process has not been discussed in detail since. Thermocouples provide an attractive means for con— verting heat directly into electricity. There are no rotating or reciprocating parts whatever to wear or to require lubrication. The application of thermocouples to electric power generation has been worked on by various (1) Ref. fi 135, section 2-31 (2) Ref- # 13. fi 115 (3) set. i 115, # 117, a 118 r investijators since at least 1890,‘ (2) and is now being The recent increase oiven considerable attentian. in i terest in thermocouples is due to two factors, (a “5 {,1 increa ed scone of potential usefulness add a bett» " V I ~ '~ ‘ ‘A .‘V v 11 71' r p . *“Ofileiafi of the nature of serictndactors. lhe eftlc- ' . . L‘. ' 1, , F. a a - 4. , 1 .1 lencv cf tcerroelectric lonoritors is :ot, a, the -, high enQUjh to make this tyre of can- 0 ,,4. m-..“ n-,° ‘ . .. .,-.V.' H v—rter ce ,ercielly feasible. uture disculsien of tee a ’- ~-\ v '- 'r- - ‘I + 1 I ‘. r“ eiticiénc; and an~licatiocs of thermoelectric bener- '( A_ ,\ rs ‘-"\,>, C1140, glLA, 5411]-, #117, HISTORY The thermoelectric effect was discovered in 321 by T.J.Seebeck.(l) He found that if the junction of two dis- similar metals (or any conductors) was heated, a voltage was genera ed at the junction which could be measured by connecting a suitable meter to the other ends of the wires. P3 1 “a f «9 rent metals which are joined toiether at one end (1. wo so as to be used for generating electricity by means of the thermoelectric effect is called a thermocouple. It was not long before thermocouples were widely used as a means of indicating temoerature. Thermocouples can be I. installed in such places as furnaces or under.: round 3Hip s, and the temperature of the couple can be read at some re- mote distance by means of a sensitive electric meter at- tached to the thermocouple wires. ) The converse of the thermoelectric c f1ect was detec- ted by J. Peltier in 1834.(2) He found that the flow of current through a thermocouple either heated or cooled the junction, depending on the direction of the current. The usual joule heating is a much larger effect, however. The cooling due to the eltier effect is not larre enou h to be of commercial use. If the Se ebeck and Peltier effects were the only ones involved in thermoelectricity, the curve of emf versus (1) Ref. ¥ 128 (2) Ref. ¥ 197 L I) temoerature rculi be a str aijht line. The fact that son effect.(l) The Thomson effect is simply th Wherever a normal gradient exists in a conductor, and 1 el :redient a1so axis ts. The volt ‘ L) O 1 O I) :75 ('f' 5... .1 F" ctri nroduccd in couoles due to the Thomson effect is usual— ly much smaller than the Seebeck voltage and is usually thermocoueles when power gen- Flo ( D fl3 O "S .10 S + 5.4- C) ,3 considered. For a br of apparatus for demonstratins these effects, sce.ref- J (D rence s {165 and {1 71. The first apnlications of thermocouples were in tem— per eture measurement. Webster defines a thermocouple as a them oelectric couole used for the measurement of heat. 0] for indicating temperature and radiation, in A. in am an. (3 general, tr e thermocou e le .as received a great deal of (1.) a attention. some of t O r. ,. \ A t duplications incl de measurin3 hum an body temperature., air velocity, and stellar temper- atures. a great deal has been written on various the rmo- couple alloys, thermocouale stabil ty 1nd linearity, pro— tection from oxidation, thermocouple instruments to meas- ure rf currents, notentiometers and millivoltmeters for thermocouples, thermoelectric temperature scales aid AA IU H V\_/ D ,1 f. ? 126 f. ¥ 47 other applications. The use of thermocouples for producing electric pow- er from heat has been considered for nearly 100 years. The method is attractive because there are no moving parts and the conversion is direct. Until recently, an efficiency greater than 11 had not been achieved. The latest figure is 7;, obtained by using a PbS - Znsb ther- mocouple. Due to the high electrical resistance of pure PbS however, a commercially usable thermoelectric gener- ator made of such a couple would have to be quite large and bulky to maintain a low internal resistance. Re- search is being carried on continuously in an effort to improve the efficiency. This research is both experimen- tal and theoretical in nature. GETZRAL DISC’SSICN There would be many applications for an efficient thermoelectric generator. In the automotive, railroad, farming, aircraft, mining, stationary power plants, and other industries such a generator would be most useful. As a means for extracting power from a nuclear pile, thermocouples present a simplicity that cannot be dupli- cated. F0 complicated heat exchanjers, turbine, and gen— e ator would be necessary. When a nucleus splits and gives up energy, the energy appears as radiation of var- ious wave lengths, and as high velocity electrons, neu- trons, protons, and other particles. To make use of this energy the only method seems to be to stop the particles by collisions and utilize the heat produced. The cross sections for neutron absorption, as well as the properties as a moderator, f the thermocouple materials must be con- sidered, and also the melting points. Perhaps someday the thermocouple junctions themselves will be the source of the atom splitting, and the energy released would ap- pear as an electric current with little harmful radiation loss. Whenever there is a difference in tem;erature, there is a potential energy source able to energize a thermo- electric generator. Such sources of heat as the sun, anyserg, volcanos, earth heat, cold sprin;s, and nu- clear piles may someday be the energizers of thermo— electric 5eneratinfi units. Even the radiation from a distant star has been made to genera te electricity by (l) of sen nsiti ve thermooiles. A thermopile is a *3 (D _.) :5 0') other than a minia cure thermoelectric gener- ator operatina at a very low temperature difference. The efficiency of thermopiles has been considered, but power is desired. The usual thermopile efficiency is around .905 T. The Army and Navy financed some research during the war to develop a small . mn rater unit. Some of this re- . (3 search is still 301n; on.‘ \J The adva nte'es of a thermos electric generator fit in nicely with some of the mili- tary requirements; namely, simplicity, ruggedness, quiet operation, a source of pure 3.0., and a source of heat to be used possibly for cooking or personnel comfort. A thermoelectric unit to attain maximum utility would also have to be compact and li3ht, and fairly efficient. An efficiency of 8? or better would :efinitely be satisfact- ory. The PbS - ZnSb couple gives an efficiency of 7% but the size and wei3ht of such a power couple is high due to E1? Ref. # “7 p. 395 2 Ref. * 47 U. 1294 (3} Ref. .f3 #131 ,WJC -12- the resistance of the materials. 'here is good evidence that the thermoelectric ef- fect is not entirely atomic or molecular in nature. The (D mf is affected by various mechanical changes in the met- 1 s‘ch as impurities, heat treatment, drawing, rolli 3, S" m pressure, tension, and magnet zation. Efforts to find an equation relating the thermoele - tric voltage to the other constants of the atom cr mole— (1) cule have not yet been successful. Telkes gives one equation which is not completely accurate as regards ex- perimental confirmation. It is 9 = i A: + Const. where, O = thermoelectric $305331": 4£=ener3y level difference in electron volts, T==temp- rees Kelvin, eo==electronic charge, and the g n A ‘6 '6 constant varies irom lu8 x 10 to 172 x 10 . There appears to be no simple relationship bet- ween the emf and the other physical const nts. host investigators have corsequently urned to long trial and error experiments to find the alloys and cospounds which 0 will give the highest efficiencies. The therioelectric properties of most of the ele cats and many of the alloys are given in the International Critical Tables. A portion of these tables is :iven in a later section of 7 a V this thee S. l.)- the metals. Compariae the thermoelectric propert ie LO (-— O (i I of the elements to other properties of the elenedt. not sh w ary relationship betweer the two, except that no metal which exribits a high thermal emf is super- 1 conducting. ne sigflni ic nee of this is problematical. p Assure that for certain theztocouple the resis- m tance drops to 10 15 ohms at 4 K, and assure the emf does not reach zero except at O0 K. In outer space one junction could easily be kept at very iiezrly O“ K. The other junction could W ave the radi tion fro1: the sun focused cn it and the temperature kept at 40K. If the couple wires were quite long, the heati15 of tze cold junction would be unimportant. The current that could be so produced by the resulting volta age i5h t be util- ized through a transformer, the couple actin3 as a primary by a periodic variation of the rot junction tempera ure. Any heat engine that can work with 00K as a lower liznit of temperature and can expand to C psia will be very efficient. Actually, little is Known about to permit superconductivity may also reveal sore o (1) theraoelectricity. In the pest, most of the thermocouple research has cm 1.) been done onmetals1which are relatively good conducto“s. (l) Ref.¥ 71,P. 315. -lh- It was realized that in order to obtain large currents, large conductors would e necessary due to the small thertoelectric voltage. sor example, if the cougles are large bars with a total resistance of .001 ohms, and the generated m"f is $0 mv, the current will be 53 sips. A striking laboratory demonstration have: use of the large current to illustrate the thermoelectric effect. The current is used in an electromagnet to support very heavy weijhts. If the metals are not good conductors then the size of the conductors beooces impractica , especially if the re‘al is expensive or heavy. For this reason, most of the metals considered in the past have been good con— ductors, even thoufih some semiconductors five mucn higher 1 voltages. I*ecent work his shown, however, that the con- ductor metals do not offer much opportunity for inprove- ment as regards efficiency in a thermoelectric generator. This will be shown later in the mathematics. The most fruitful ar of work now see 8 to be with (D is \ semiconductors succ as lead sulfide,lead oxide, silicon, serranium, antimony, bisruth, carbon compounds, and .4 rt :3 J t .J , J U) ('9' H O (0 O i O (D 3‘.) The chief disadvantage in using a semi- conductor is its electrical resistance. however, most H O to H *3 «D (I) H- :0 (‘f- 1,. .3 C‘ J LD 53 H U) U substances whfcn have a nigh electr have a high thermal resistance, and a high thercal res- istance is desirable to prevent heat conduction along F4 Ken I the cou: le . The relation betwe electrical and ther- (D :5 mal conduction is known as the Weidnann-Franz-Lorenz Law which states that the ratio of thernal to electrical conductivity is eoual to a constint tie the absolute temperature. The lower the value of the constant, the better for theroo ocoupl3 purposes. However, for most materials the value of the constant is the same, namely 2.45 x lO ’. No materials show a lower value, but many show a higher value. The diff erez‘ice between and the value for the material in question may as called the deviation, or b. The larger D, the less desirable the material as a thermocouple for a power generator. Papers on the subject often state ranz Law to hold". This means the value of the ratio of the r:Ial to electrical con- . -5 - ductivity is a may -i.r un, or 2.45 x 13 . This condition (9 U) limits the number of suitable naterial3 and serv. as a usetul criteria to judge whether or not a certain . stance might serve as a power thertocouole. Conparine a metal thermocouple to a sonico oniuctor thermocouple, it is obvio s hat the fetal thermocouple will have a lower resistance for a iiven size. However, there are two advantages ior the seniconductor. First, the e“f is higher by a factor of 2 to 10; and second, the electrical resist; nee us uallv decreases as .oe teno- oes up. Also, there reéaids the possibility that the resist1nce of 1 semiconiuctor zn1y often be 4 ‘. . 5‘ r 1 'v v. #1 5‘ a“ c 4" 'y “ 1 +’ I‘ V‘ o lowere1 coasileraoly wluAOut affECbiJD tne oohe ~.ro—- 4-',~~ n ‘n ‘1‘.- ' . .9 ~."~m .~~-e--- “eruieo verv "uci, c- the 111ition CL oil;flt 1nounte C’r O U“ (D l.__l '4. t’; H (+ (D p, (+- 0 FT’ :elow 3?, most of too work tol J i (I). f) (D E?- *‘S H :3 (1‘) O :3 U) (D S. O O :5 1.11 O Q :‘S U) C+ DJ (0 CS‘ 0 L3 (D (—34 (h H -) i n) to find ‘43 semiconductor with 1 3001 thermal emf, a low he1t conductivity, 1n: 1 low electric1l resistivity. neceut dork in:.icetes that the - properties mitrt b: 1tt1ined by the agdition of sm1ll 1mounts of ”impurities”, in some 013-15. ?or ex1z‘1pl conductivity of silicon witlzout 1e creasing Q, 1 31111 . - ‘ 1“ --. A x P‘I r'\ r' W ‘ ‘fi 1 "I r‘ r " I' n‘. ’ ‘ ‘ ‘ ‘ amoun 0L COyguT 1 Qnt oe 11311. The tpr 1nJ 1noont of met1l to 111 is i0“i1 omiy oy exnerimental work, however. See Ref. ¥ 2 . Tue physiC1l intororret1tion of coniuctivity and 4.1,. -.w.-»'7 «1‘ '— -"~ 1- 2n -~.'.'v~.- 5» .~« -~ onerm1i Sui in sex iCOHo&UbOID is Leiné qevelotei, usin: the modern theory of soli1e as 1 1weis. See ‘1 .0 . A “1152 :2 ’3; J")? 7. fr". . _ . - U. ’3 {3| 0 ’3 _. v", ‘ - f..— o- hm? , ' ‘J _ r) 1 '7; .1 14"... xii 01-1058 vi; \J , LO, '1' ' ll 1/, )"JE' , 1 J , -w ~vL 7%,) O I no f1r, no one has cone forth with 1 complste theory. ‘ -: .- . . r ~ wjicn re reeen s carrent. A toermocouple to set no 1 loC1l emf. It is known that the emf ‘- somerCLt :31111 cu: to 1 semi—perme1ble mentrune. At the other junction, 1 local emf equ1l to the first is set up 0 posi113 it so that the not emf with the circuit at one tenyorature is zero. emf is called the Peltier potential since a unit onerge in crossirr tne junction will either f1in or jive up ne difference in the Peltier potentials at the functions 3 the Seebeck oltege, often 011111 the Pelt 1r voltege, 1nd is zero when there is no tem- perature “r1iient in the conductors. Shen any two met— go H m x ‘D nl1ced in contec , 1 potential is set up oetw een the other two ends of the metals. This is called the cont1ct rotenti1l. The absolute value of the cont1ct notent 111 is difficult to measure since it is 1 sen- sitive function of the surf1ce condition of the metal. The contact “otential is 1130 nailed the volt1 effect, volt? notentizl difference, or “otenti1l function. hio nets-on the contict no- Ho H- There e r 50 01’)‘ U) (D s 1 clo lat tentiel end the Teltier voltage. This rel1tionship h1s been develope” from thersodyn1ric1l consiieretions 113 st13\7:: 'here V - cont1ct notenti1l, .1—13 _ 5T T‘ T : temnereture in degrees at solute, and P = the Pcltier - a .. H - ent glue 1 suriice he1t of char inw coeffic- Lccordin: to the electron r13 111logy, it appears would be quite iifferent when in the liquifl state. Very little researcL has been carried out investigatin tie thermoelectric nronerties of liquid - liquid junc- tions. To nrevent the junction from becoming homo- geneous by diffusion, some tV3 J- (D of separating membrane \ should be used. The el ct a) "5 o-chemicsl effects day be- come large when the substances are in the liquid state. Excerimentally, the electrical conductivity has A J no relation to the thermal emf. Now, O'- e‘Ilv , - .:.. T" r11 Vii L where cr 3 electrical conductivity, e : electronic charge, N ; tne number of free electrons per cm, 1 = mean free path, V”; average electron velocity, K ; gas constant per particle, and T 3 the absolute tem- perature. Since 0’0: va and since the thermal emf is not proportional tocr, the thermal emf is not pro- portional to va as might be exnected from the elec— tron 31s analoty. A paner by Ellis states the most important char- acteristics of a thermocouple to be used for power (2) nurposes. They are ”(1) maximum hot junction nJH AA vv 1U CD "'3 an»; Cfi -13- .4 , (2) potential characteristic C.- 'U i d H) *‘5 ('1’- CI *3 CD 0 H *2' r3 ( 3 O "J of 600 ricrovolts per degree C, (3) the structure should bc nechanically strong, (4) low internal re- sistance, and (;) srould resist oxilation over pro— F- onjed periods." Cther desirable features are com- pactners, light weight, reliability, simplicity, and low cost. Ellis also states ”The examination of the characteristics of metals indicates that a combination of metals would not produce such a couple. The best approach may be in the field of semiconductors, in- corporating trace elements to adjust properly the ther- mal and electric1l conductivity, and structural char- acteristics. The application of Quantum mechanics and a complete review of materials by the application of the electron theory may result in a couple whose lattice structure has the ootim‘n desired caaracter- istics." Fe oes on to state that such a generator, with an efficiency of at least 8%, would revolution— ize conversion units in the power field. The poten- tial characteristic for metals is at present only about 1/10 of the desired bog/xv OC. fihen a desirable couple is found, the desi3n of the generator unit presents itself. For small units such as 1 KW, exposure of the junctions directly to t‘j (l) the heat source mi3ht be satisfactory. or larg r units, in order to maintain a constant and even tem- perature at all the junctions, a liquid couli used as a h eat- transf 33e nt. The sh pa of the unit might be cylindrical, with the hot liquid on the inside flot- ing cast the hot junctions. The external junctions could be exoosed to a blast of cooling air or could be cooled by another liquid. This second liquid ri3ht be used to heat a second unit, in this way conservin3 more of the available eat. The design calculations of a soall unit are ;iJen in detail in a later section. There has not been a 3r33t de3l 3uolished on th. moelectric 33 ner ators. The bibliO3raphy lists most of the books and cerio: ic als which contain any u,r— vw ‘F ' (l) '7‘ H ‘, sn -'3 X 1.14- r: 3 3:3 ,- H tinent into :3cion. lhe Industrial ; t Index and the "En ineerin: Index" contain nun erces to thermocouples, but most refer ments applications. Such things as acc ity, oxidation, ani response time have been fated thorou hly in relation to te oera I" ment applications. There are three l3ws often spoxen erous refer- to +“e measure- L411 uracy, stabil— investi- ture measure— of in describ- in3 thermocouple character is tics .(2) The first is the law of the hom03eneous circuit: a current cannot Le initiated in any circuit of a single howo 3eneou metal by the application of heat alone. The "econu (1) Ref. 3-, 323. 32 #35, 3:7, 310/, #117, 3120, 31:1 (2) Ref. ¥”7, p.80 law is 1s f3llows: the elmeoreic sun of the th (D ID13- Ml ctric volt es in any circuit of dissimilar metals at a uniform temoerat ure is zero. The third law states: the total emf of any number or +nermoiunc+io.“ in series, at any set of tr emoeratur , is the algebraic sum of the iniivif usl junction emf's. The couoles are all assumei to be of the same two me tale. The second 13w is called the law of i. e ”meiiste metals, ani the third law is cellei the law or successive temperatures. These three lsws h ve be en repe3tedly verified by ex- it} '. \ lkJ TV" "W' ‘V:: V“ ‘1‘.’. r‘ A T '3“ ," 1'13"? ’1 1\ ‘n #1 ‘ '5’: \' ‘ . l. v ‘ L) -r— LL- . 4—. s'.L-.. .4 -v s. A“ an I hJ A A -A .L v, ..0 Several exoeriaents suggestel suitable research worL. One was t measure the emf as a function of the dis tance across the face or the junction. This was readily done. The th rmocoup le wires were about 1/3” in iiamet ter, of iron and constantan. One end of the iron wire was made flat and smooth. One end of the constantan wire was made pointed and share. These two ends were then placed together in a constant tem— perature water ath, and the thermal emf was measured as a function of the distance across the face of the iron wire. No detectable variation could be founa This was as expected since the iron wire was fairly homogeneous. As another exoeriment, the effect of nressure was tested. Hitn the constan .a point touch- ing the iron wire at a fixed point, the fressure at the junction was increased. No change in emf was Observed for a range of nressure from about 10 to Another e? .neriment was to Observe the effect on the emf when a current was passed transversely across the face of the iron. Fig. 1 shows a sketch of the asparatus. The effect Observed for currents up to H 5 sans is shown on 3raoh 5. The uovard curve of the current indicates that the sliyht incre2se in en i at the face of the iron conductor. The use of transverse current to produce free electrons does not seem to have any appreciable effect on the emf. Reversal of the transverse current produced no change. The idea in this experiment was to see if the conduction electrons 2_ illilll~®3>~<$~r Wa/er F: \—_J' Calls/anion Con fer/ner- F/g /. set in motion by the transverse current might act in reducing the potential barrier at the metal surface which limits the thermoelectric voltaje. In another eXperiment the iron was heated to a red heat and then touched to the cold constantan. The resultant emf observed was that corresponding to the averaje temperature of the two metals. This show- ed that the "338" pressure set up in the hot conductor was freely dissipating on contact with the cold con- ductor. An equilibrium temperature was quickly reached as exhisited by the average temperature emf observed. ihere seems to be no nossibility here for increasing _?4_ Since the efficiency of thermopiles is of the same order as for Ltrge r generators, the size of the junctions app.3. rently has no effect on the efficiency. The metal couple composed of Chromel P and con- stantan produces about 40 mv at a tem Mp rature of lOCOOF, as shown on graeh L3. This voltage would be sufiicient to energize an efficient thermoelectric generator if it were not for the high thenrs l conductivity of the metals. There are at east two methods of decreasin the thern.l conductivity without decreasing the elec- trical coniuctivity 3 co'bira le amount. Ihe first is g to find a new metal or s -icon ndu uctor with the desired m characteristics. This is the present -venue of approach. The second oossible method of preventingl neat trans- mission is to rescve a section of the metal and put 0 de- U) in its nl3ce a heat insulator. Eiow ever, this 31 the electrical conductivity, excep t «hen the U) C II 7:1. S 3' (D insuletor is such a material as 3n ioni bed gas at low (n preS‘ure. Such a gas will transdit the current, under certain conditions, without exhibiting an excessive— ly hifh resistance. Eiternsl means would be nece ss- 3ry to keep the 12s ionized. The only heat passing through the gas would be by radiation and ion bom- bardment. 1'his heat would probably not be so serious as the conduction heat, depending on the ep3cing and 1‘) K.“ tenperature difference. To keep the resistance low, a short spacing and larfe areas would have to u used. It is doubtful, however, if the emf would be large enou h to cause current to flow in the even if a high electric Iieli intensity were produ- ced by using points and short spacing. Possibly a (D O *3) 6+ 5‘ (I) H O :3 l liquid could be used in plac ized “as. If a solid were used as the insulator, the iarse temeerature drop across the material would in- roduce a new emf which would have to be cons dered. It turns out that the thermoelectric properties of the stance with hijh electrical and low thermal conduc- tivity. The efficiency of the Pbs - ZnSb couple is 77, A fl -- 11-. r. (l) W‘s» n ‘ ‘- v“ “”1 as resorted by Teiaes. this is the ooserveu efficiency. The calculated efficien y is lQT. 1'0 increase this efficiency and reduce the size of the coub es, a higher electrical conductivity for the PbS must be obtained. This may he done by adding small amounts of another metal such as silver or copper. The effect of such additions has not yet been fully determined. The best method of doing this would be to add the powdered metal to the powdered Pb3 at room temneriture end then fuse the mixture in a ceramic boat. 3 (1) '..E.‘:f. 1 ‘ii: 93 ‘ o N Om Due to the hirh melting noiht oI Pbo, 1500 c, it is \— difficult to work with it in the molten state. seat of the thermal emf, it might be worthwhile to investigate the effect of costing the face of one metel with various oxide films of other metals. This might permit a greater emf to be developed. A useful investigation would be one to deter— mine the reletionship between the wavelength of the heating radiation and the thermal emf. This could be done using a light-ray apparatus as shown in Fig. 2, for freduencies near the visible region. l'he enjle of inclination of the grating determines the wavelength U ||| by the formula nA=2dsine, where A: ‘.-.'s.velen";th, d = [5}; 7‘ Source ruled line L0 nscing, and e = the en le of incline— ra- x.) mermaroup/e tion from the horizontal. F77! 2‘ the order of the re- flection. :or higher freduencies, en X-rsy apparatus similar to the above light ray apparatus could be used. The per cent absorntion would have to be meas- ured by an ionize ion chcmber and allowed for. The relation between intensity and emf would also heve to be studied. Another interesting investifation would be to determine the effect of various energy electron beams on a thereocourle. A thermocouple recoonds to heat, unich is an tion of the atoms in the metal. It might t (4 D "S J L) 3 .L.‘ ( be interestinj to Observe, if possible, the effect of a neutron beam on a thereocounle junction. Some of the neutrons would be absorbed and scattered, impart- ing a hifh velocity to some of the atoms. This would‘ cause a temperature rise which mifnt be measurable. If the two metals were of different atomic weights, there would be a flow of oarticles from the heavier to the lighter as shown in the following analysis. Let Vr = recoil velocity of the atom v1 = initial leutron velocity mass neutron = l m = atomic weight of atom N = nunber of neutron collisions It can be shown from conservation of energy and momentum during an elastic collision that, VI’ = ___£__._ V1 (1) m+mo Assuming the number of neutron collisions to be yro- Jortional to the atoric weight of the target, (the number may not be pronortional due to the density or . due to the resonance levels), then N .. Km (2) The flow of recoil atoms pest the junction can be rep- resertsd by i which equals the number times the vel- ocity of the atoms, or 1 = Km Emovl (4) {11+ mg— The ratios of i for two different mater’sls (a) and (b) 313 I K3 m3 (mb‘rmo) 1~ Eb mb (ms+mo) \ -) be carbon (m : 12) uni material A H U” (0 v C" U E? (D Q: c+ H m U‘! P) >2 H- n; "J [.J :1 ’\ 3.0 I [\3 ( ) C\ V o .3 T5 (D L5 H D "4 H (L) 'u C) .Q "g D C O O in) N] I , P" U ' N 0.0 I\J C) L5'\ l—J U4 *X‘ (D U If KD end FD are equsl, then t1 atoms from (a) to (b) is 0.9?7 times the number from (h) to (a). This small flow fro“ the heivier to the ligiter hetal might be fletectesle as a current in the wires. This methoi of ietectinz a neutrvo team could will now he nonsilerel. short rect3n*“lsr bars of copper and constantsn will be used as th; couple me- I" H -~“ '1 -‘ -w‘ nfiL‘ A... 0: teriils. :or cottereconstantan, about Q.q34 mv/ C, or ?7 mv at 60003 is the developed voltaje. To be enerdtor voltege should be at least 34 volts with no load. This would require The sides vouli be made of some heat resistant material such as transits, with holes in the sides for the square rods of cop— \\\\ oer and constantan. The heat Hea/ Source f77u3 would flow on the outside.Tne inside could contain water to provide a cold junc- tion for the thermocourles. If $90 counles are re- cuired, 222 couples will be nlaced on each site of t nyrarid. If the cross sectional area of the rods is 1 cm; aid the length is 4 cm, the total area of the O . ' ‘ 2 holes in a side or the nyremid is 232 cm . The sides H) o the pyramid will be trian these triangles be 250 cmz, then the ratio or holes to the total area will be 0.3. If the trianéles are equilateral, they will be 94 cm on a side. Assuming the hot junctions to operate at a temperature 01 130000, the electrical resistivity of copper at this temnerature is 7.;5 Annwcm. If the cold junctions o . are kept near C C, the resistivity ( ) of coooer here is 1.72 /an.—mn. The averaje vs us or far is 4.5. J ,4 ‘4 ,0 FJ C D For ccnstantan the averafc is 50.?. The total resistance of one couple mar now be calculstsd, know- ing F , the area, and the length. The resistance is 9. 3 x 10 ohms. For a total of $90 junctions, the overall hot res stance xill be 0.194 ohms. The current I m‘ AL delivered to a .l 4 ohm load will be V) (N 2 C" 1 L LJ. t s n If). ‘i 5;.) '( load, the maxinum power condition, the generator ter- minal voltuje is 12 volts end the cc.er deliHrer: d to the load is 7A6 watts or 1. Che. This is the cutout pom- er. Next, the equivalent innut power must be found. The thermal conductivity of cooper (K“.) is 2660 2 . (1‘ BTU/hr/ft /°F/inch. For constantan the figure is lbb. ’ Converting the above values of K and using a tempera- ture differential of 133000 as a basis, the heat con- ducted by the COpper “5 /min and by the con- stantan is 0.0 BTU/min, makir g a total of 9.15 ET U/min being lost by conduction to the cold junction. For b90 junctions, the total heat lost is 8150 ET’/nin O r 192 hp. This is effectivel3r, the input. The efficiency is then 1 From this it is seen C: l [- .,.. :3 - 0-)“;— v that the efficiency is about one half of one per cent. In Dractice, this might be increased to one or two (1) Ref. ¥ 13% sec. 3-25 J -71- g.‘ - 4'.“ 1 - ‘ .- A ,\ ‘ ‘ bv USlflJ other meesls hltfl . niche“ vol*i’e. uucn s ' A - . A ‘ . + p 1 ~ tie-:;elsctr3c gen resor hit“ 3n outpue o; 1 en ini A '1’ ~ ‘ . A “ an ‘ -‘ U - T5 haww/ lbft zhin‘ FNC fire-y, UJErFV. ~T¢ The thermodynumic ener y function (12) may be enplied to find an independent relation between 17' sndAm yr A... .4»: V V 'in (13) is the "work function”, somet mes celled Thus fiy':7r (13) The internal enerrv U reoresents the difference in '1 (7+ 33‘ (D (D lectron srecific beats of the two metals, times the 1bsolute temneroture T. U : £30‘ T (14) This 11y be seen more clearly from the following diagram. Consider an electron hissing from conduc— tor l to 2, with a random W/A\W VElOCifiy v. Then the in- ternal energy of 1 due to f27z‘7 the electron is U, : v,Tfi3 The internel energy of 1 due to the electron is ’51-.- v,_T,¢3. . Therefore, U"- U‘ 2 V,T,(C¢‘-0’£) :: U (15) U,- U, represents the net internal energy. she random velocity will evereje out to be unity, hence U -,A69P (l ( O‘ T From (12) my- —A','. — (1) CL H H \J 7 If the work is zero, fl — C, 1nd F‘- :T= 24,34 5. Substituting (19) into (12) gives \ I V:U+ le< dT which is called the ?ibbs-Helmholz equation. Now the equationry~= U — T 3 may be rewritten, uoon substituting equations (13), (lo), and (19), es 7/“: AU‘T + T :3_I_r (30) 1.1T OI”, AU‘T : 7f - T :31. (3].) df meo, g%::gy+4, (6) From equatiowe (o) and (21) the values of-n'endbo' can be found’ From (6), AMP: E'L (2?) dT dT Substituting (22) into (21) gives TE-TQE-W-TH dT dT dT from which F‘: T GE (93) dT This oives the exoression for the Peltier coeffic- ient]? . EXoerimental values substituted in for \ ‘7 9nd T jive results “roving this ecuition w thin the accuracy limits f the exceriment. 1he value of fl'cun be determined directly by exceriment, but rrecautions must be taken to neutralize the Thomp- (D on emf. Substitute (34) in o (h). Then I l 0‘, b 9 1T 01" .ir_ 1r r40‘ (”95) 7n - ‘T From (23) A I U UN \J Suhstituting (9‘) it 3ince z; - £3 (94) T - T Equation (27) becomes L's-v T d L : -A0" —3.'. dl 01" 1 (3 E n\ Aa‘: " T Eff-3" (20/ This is the final expression for.Aa~. The two -43- O O (U r.” H: H (v) H ‘J L3 (1' k I and A0“2re usually obtained by ther- mal measurements hut may be found from the curve of I. 1.: OK. (T, - TL)+ rig—gm, - T‘) (2') \x This may be carried further, and 13 sometimes given 9.0 7* 1 'T‘ 2‘ / 3 4‘ " '7‘ (TI " T2.) + (”76(11 ’ TL) +2“ for; " Ta) n the The constantscx ’F , and ['can be found fiov experimental data once three values of E and the cor- responding values of temperature are known. A simul- taneous solution will then give as and 15 or mud, and f. Assn-ling- 0k and I! to be known, to find 77'or Arit is necessary to find the first an? second derivatives of voltage with respect to the temperature. v"andznd* are usually evaluated at a fixed t moerature such as CO C. In such a case T, — T1 = C, and d .ok and p. I H! m cf"; :‘3 from which 77‘: Take-and 4,: - Tf . The nu- :11”— merical values of ar and.Aa~are usually given in mi- crovolts per degree centigrade. The difference in the values of v‘for two different temperatures is approximately equel, if‘oa~is small, to the value of , . - A - t p , '7 15“.-. ‘ o. For examole, the eat of a on — to couple at “H p l I p of W‘ for a., 'i‘h Pb .' A reference metcl, at SOC, '13 foux1 fro" a and b, 1..) 777 = 373 X 3.26: - J57. At lococ, fig: 373 x .CJH : 1143. The 115 orence bet‘..‘een 7/;and 7r._ is 335 microvolts, 23111011 is only about 2* d fferent from th; value found by form 413- , h H F‘ ‘+ D. L ‘ a..- ‘1 A‘r The -oitier he... coef11cient, or 77 , [Mlv'C-Eo -.. }_Jo . anct 311 for j...)- '1 ,4 Ho 0 ‘3 ( t‘ H O '— ,_J O *- r-f' 3‘ 01 ”.D B H) I -1 (L' S \D *‘S }1 CL (D Ll; c+ $0 (_Jo a given tenrerature of the junction. If the Thomp— son effoct were zero, the curve f E vs T would be a straisht line, and the value of 77i -W‘, would eoual E. 13 .h er found fror beat measur=nants " - fi‘ '2 v “ 1 "P‘ a! . 1"".":‘ ‘7 r r‘J“ N 4' I or by calculation, tliqo a iair escroaimation to the attainaole emf of a thermocou 'd I...» (D I-r O ’S :3 O C. (—{u J (l) r +- v) H 0.1 ’ '1 :nere the Thompson coefficient is large, the curve of E vs T vill be curved_ehm. fl7- Z; will not eoual I :3 U I ro \l \ \l A I O H H \ ~I II I K)! C 0 EL In.the above examole, 77" and 01- I H or Ar: 11.3 . New TI‘J-A" 1e 30: + 11.3 - 316.3. which is closer to the value of E (512) as found by the o elratic formula. The cuadratic :tio;1 e133 ess- es the true- eztvf versus T. The val es of 77‘ .'.-‘:.ndArare a first and secon‘ agwroximation to this 3. Another derivation for 7r e_.dA<7' starts 'ith a )I "f closed Circuit of t~o Sisc1vi There is * ten eraturv fiffer 024A7' ”01- ,T+AJ' F+AW B 0;.AT fagzza Substitutin: (?9) into (31), 73:77; T2. 1‘. 1 (v ence, I ( h 1. however. tdiing the enf's around the circuit, A2: F-l-AT = .A0*+(¢€?- d;).AT 3;; W‘ (571-03) d3 - d? t‘ *1 uLfl+Ar -—oW cmaAT T-I'AT T Tffl 2 “here o = “nit charge .4 l 1’07: -0§)AT = T T +, AT 2 (GE-0‘) ; .“ r1 “LL; ..F“+.A6” AT ~63+4T '5. l t K»! \. KM \N (A -+:' \N V v v U‘l ., > 7 2 I .1 1... \ l: n a G “.15, 0—4 - 11C. -1. .. a 31‘ “I ‘11 .7 «¢ \1/ C A. ( H- . .r. 1 i d T. (2,1) : rid- ( v. is ous an;lys «V. m- . J. Lu») L..Qr ou“2 ‘ Liu I. n J. -r A‘ . I — 4 *F’\“1 fl. OE We \J'. a. m; C x; w. . C C ‘ Jr. ‘71". A 7‘.Ya L 1/7.: 71 .—V r) (adv ,—_-.C‘ + k _ k. v V Cv‘.‘ V, 'v‘ R t ‘ “< '_/ _. ‘ 1"e. R. . 3 o, ‘l 2/ 0011771- -uvuvlu r} C "r tL 5 (v 1“ I). ..\ p: 8 C :L A: AI» ‘5 Lle 9 VI“ W .1.‘u.L-1L J. .o , .'. OT TILLX“ no.7 -y“- v1 ‘1‘- .131" V“ a v ... A, J .‘ -1 4 '3" 4" tion howe1 .5? - 4. . l 3333' , 1-.“7’291’1 iiga-xa A K“ \J .‘ J. A v eff I d 1 ”1’1 ~ ~ \m .-- v .A‘.# l 1 1r r1 LJ .3 we}: '7‘ r‘ ..‘ _I‘J a v5 .1-— ‘1' for .1 O m 1 l ‘g—‘fi r+. .ter .1- ‘r L LI. 1. Q. .1 '7 L; 51-94.. '."\ 4 ~-» ’11 - ... ”ill be 7.7 couple ‘ Pools b.‘ WI x s--‘ . If u ut to ‘r 1.71”“ C‘ in; L i; "3 14:4— 1 T 31102 9 Mg (0 9‘1- L; T Y.) _ r. '4- . V a --\ n1 - exteiual re istauoe Z“ = total out/“3* e1? 11 = :Kfl; junct1411 tan“. T, = cold j‘notion tech. AT = T1 - ("1 ‘7 = overall efficiency 7r= t‘~we1 efficieicv I I/ "' V A .-- "‘fi 3 . . ’1 1‘ A y-fi F,f’- average s ecifio resist;.ce of co ,les I q Ir - l V- K . n. ‘ .\ '\ “'\ 4' . w n,h - averaie soec1-1c neat cohiuction of couples '3 1.",— fiW’\"‘" r— . -\ . n" ' r - '1 e,, - o-o~: sectional area of oou lee L = 1”: th of both couples “ A . PI 3‘ ‘ A 'W ' " D ' ‘ r. “ V‘ » .r- 1 p Tn; first etec o to .1nd ; sir 1e relation ior the efficiency. 1 l ELt==1 “‘ (1) Lfi rfi“ ~\ p187. SI :L"L RI 1 (“I T—-_-. .l\ -L'f'fl'a ',7 I1: ) m A I ) '2 buff 43d: ‘75- + «a; \3 AI‘ 1" ’ “ uron (1) an' (1) To ‘1 D o. n. n. r U ' ) “.‘f-‘f‘ $33.}- ..'.3. 47.} + .C,.f = 4.,J £1 + _._.- (4' -\' 43.. _ s! n ' eibet tuie (4) into (3) ,f t: ' .50 A r: fie - lxl+ 1.»; Illlf. 11 +q,‘ (J) 3 —% 1.: A1 I'T'3‘1:«v, [4/ - n1- . o E‘ Pfi'n 1 - Loaf: ‘L' -= ‘ . ..‘ v.‘ ‘ :3 —~. 7 I. e 1 1+- .1. RI 1' R: + AL, '35.} c 5». fl ._ 1+ 1* L T. m.4 #3 F or, 1'1 x) 1031 I 7‘” treater K 3 COH- ~e efficiency. ,- t‘. .‘I‘ l to R‘, "J L inversely broyortion- suaei. :3 (I -~. s) \l 7 I..\\ ¢ I c. E = l r O D“ .1 Wu. 8 F ATV C L 2w D j‘ -r 1&- 1* K; = :~L d ctors. #1 . I u l situe cur-41‘ (L; Li +1\ 1 ) (S) , - I a Lid. 11 = F n‘ ' IQT+23~ (1v) eel ;1102 +he *a«* ‘nrm F>ctcr3 result hem , y-l relitiore h«313: i -.i 1 \ J. :1! - if, ('Ll/ H II _‘ — P ,1 ‘ (1—1 \ ”all Tl— R: 3,: 2 AT 91' “'I Q (14) \A r"; ‘- -:.. e (4 H9? Since E=-eAT by definition. Equation (14) may be rewritten as, J l I I J’ u I / a 0 35 c1 + g ._1._ (15) R36 _ V + xx 7L d” :3. 2‘ e‘AT n r‘ v, ' ~r” 1" ' --u ' ’ 77" I, L r ac ---I’{ + ~~1”+ NFC/7' = [La-F )ifiurL‘l‘fle) 2 ZZZ" ' e‘AT e‘Al‘ - 1 7 £11252; {1”ng C(x'Pféfifiwyar-(l?) K. A? K. e*4I From the Wieflrann—FrinZ—Lorenz 11w, taking the everage temeerqture, r. -47.. V Placinfi the nnmericol value of (18) into (17) gives K1, AT y = .1 + T." Z. #1:? _ I (19) D “:1 LTL+————l+e:$ (4.9 y 10’)(T.+T, )J ihis is the final equation for efficiency, n- volvin; only the temfieratures, the thermoele tric bower e, and Hz. The value of Kz_will be discussed shortly. A plot of'7 versusA3T for various values of e is given on grifh 1. Graph 1 is plotted from equation (19) sni the curves agree with a similar unity, which is the maximum power coniition. 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Q R as & ix: 3* Q LB 3:5 \QQSEO % \ ¥Q\.\ OQNTN ‘\\\ | UoO “R .U nmmkmmh 3 mm 8m QQK 8% con. 00% 00m. 00 N. 8\ 9 S L. 8‘ ‘lOl‘ lb? 0‘ IM LCII L; . mm gum...» UT g: 01 MN» .W \A LT 6‘ 0.1 oomnm L7 5% 0‘ ogxuw NQV v 0 83mm mNQV . 8» \Q MMQ\ . o 83.9 VS w ES 0.} KS \wsak \m gtmfiu M QQM “Q .H mi $ Sufi \& «K “B Misu \SxxwtO ‘_ fi- . . flaw" FIE; ,. -o.v o a . .--_2---.. _, _....T_Q,. Q tb.\\u.\>wq “ , 8m %\ _ 3. mm 3 n N \ ol/o/ngv/Av _ .w w _ i. . . W. W , . , . u a ‘ . ~EYHNMB¢M5Q~Q§ tR-fwty :- ._ w _ an... - - _ _ _ , I . W W . . . . - fi 1 . M . _ “LEW . fl “ _ _ . _ 1: _ $.- fi$$§k>mk ._ L _ .UOQQVp-R URN-R Uo\-S\. R ... fix kméngm «fitnwwxum fiQxDSvQ xv:- m..> \v§m\uu\\m\ \o 3:: U \QSmtO 1: N 24. ‘Q,. V 7:1 ”WW? 1 i _ _ L . . fl _ . _ _. . . ._ 1.- t1 _ _ _ .. . «Hwy-a. Mx §< Q N\ 2 Q\ 9 0 N. W m. V m. .N __ b-7-“--~.——. -. _.. ! 1 A 3 $36 Sfiuté VS \3 u: 36 US muck Q§u< \wam; SEQ. VERA? try-:3 v w> 0 mmfixfix mE-VSRSENK kc ESQ \Qfimto 08.0 VNQO. mNQQ. Nms. was. $66. Q VKme k3 Sux 25 u 8N\ UK 3v \mSm-kxw .Uo 8% S Nwax u\$ wk. 8% § w-thkukfimk m.) m quh§ 335$ wSSm Sm \ L 0% \\‘m..\u_ E aioy a“- 3 99 5.3 uuafl ,3 8 0/\ a/dno 90 92 o sway/”w 4/ ¢. QM 0V. ‘ t .—..--.-—— _----_-M .__‘_._.- 10. ll. 12. 13. 17. C T V‘ ”avidson,”3uclear Reactors for rower EleCo?n$ro OCt. 1348, P0962. Ellis,e.P.,"Thermoelectric Generator Po r., V.67, July 1948, P.657 Locke,E.,”New Dielectrics,”Astouniing W V _.JJ‘- 3 olio5r1phy 1348 Periodicals . . . O 5. v? ’I '11 rillou in anl Iskenler1un,n., Lhernom H —‘ fl 'AI‘ ‘7’ 5‘, -A tors ,slec. so -u ioatios ,vPE, soot vv ”’0 arter,n.J. nethoi of so.s--uctiu- Cu- hermOCOL ples” , bci. Instr., V 19, 41, 1945, v.72. A m dbl": o H‘ Osborn,J., Mirneto.-trjcticn 1 r - v.97, June 1948, P.571. ' h Popet,“.,'Rersrks on 'The afficiency H Generators , J.A:pl. Phys., v.19, De hermocoup le Alloys” K-270 Electronics, P. enerstors”, C n , '\ I‘W‘ ' A J3u8r-‘¢ “4" v / P.300. M W 4 tic .l 3 ’ Sonstantdn :?C.1;'r:,t c ‘0’ l7 "‘ ' It “a ueSlQWS , ;lcc.\/ Science Ticticn, Elec. 77y“? of Thermoele c.1945 v.21, June 1945, V1931,W.,"7190trOCHezical Sources of Power', Elec. Engr. V.67,Ajr11 19 45, P.354. and Hay 1943 P.456. 1941 ‘SOoks Uas,”Electricity" ,1947,Thos. -urby and Co.,P.394. Hall,"Pr1n. of Tlec. Engr.? 194,, NcGra —Hill, :h-wln 1 Publ. 30., P.165. Perioiicals ?untiofi,3.,sni ot‘c "Pr o.erties cf Erium ~3tron- tium Titanate )ie‘ecfr1cs' ’ur. Stis.._. Zecssrch, v.33, March 1947, P.337. 9:51 and Vaniusen,”1be TLQTTO“1?CtTiS Propertivs of Uranium”, f.39, Eur. 3t3S. J. Resesrcn, Julyl947, P.53. CtI‘iC Vi if... .3... Ln]... 11.... 2 . “11'. - 5..., k.) .' ’1‘) H V.) m 0 ‘- O o L 3 . .\ U3 I“) :15) CA K )1 (D h . ‘m r, v‘ “.1“. '- A ‘4‘ V .. ‘ O ‘l ,A U . *3. , 3nr3vfixfl*, L.,"TbVWMY)31?CtViC “L ‘T‘ , ~ "“ v T731 :7. J. 1xptl. Lheoc ;,js. use}, ..‘ ‘ _‘ .. n.“ m 11.131.111.31", 1..., LLVS‘iZI‘Ch 001.13.; r. L. *7 r1 2* .L r J '7 -. 1 :4 .H‘Q 5: , \J o E \—" , “J jJJ't . l, -1 I , f7 . .3— .4 T ~ ‘ r- ,q m 1* v-17? . cornea“, 1., ani Lari—Loro”1t ’ t‘ W‘ . . y ’3 .. ‘ _ :1 en -er anium comic,QJuctors , ,, ~07. g. 3.4. T‘f . I 1" m " “ulp :ni err, vultifle 1Le v - A , 1 O. o' «. 10:. Arr ' «. 347. p- 41 A _.I ——<. Tr Z, 11.0, ?h s ”A -. vs" TT" 1" J'L)L).L H 11% (ill; Libau 118V o T? _ _ n. .. , “atsch, L., 1nd others, Electric Fewer ooorces ,Elec. f/: A ,5 Q L23? 0 , 1‘17 0 (LV , :Jéyt 0 19,37 , p c 83 0 Telkes, M., ”The Efficiency of Thermoelectric Gener- / n ,._ _ A ators , J. app . Phys., v. 18, Dec. 1947, p. 1116. V 1046 ._ n . . - _ - _ . 1kimov, G. V., Lethoi of Ueterfliain5 hicrothesmll u A . - --.I 3. :le , 3&3:th L‘.‘?.’l'io, (103).. 3C1. 1213.933, "if. 51, 19 $6,177.40“;- . H Frenrel, Y.I., Theory of Electric Con act between H n , 1.1, , W, K - , metals , J. Exotl. Theor, Phys. 5333, 2.1:, 1946,p. 310. _ n p . A Ioffe, A. V., Elec. “esistence of the Conta‘t between 1 \z t - ‘3 a Semiconauctor and a getgl , J. Phys., U333, V. 13, .f 195.3 g p o I 9 o 1-7 H 1 - Johuson, V., and Lark- Horovitz, 1., Theory of Therro- ' vv " P (f ‘ €11,0tr’1" 11.0.31" , Thy-g o RSV. 1'7. 69, 191": , 1.). 2590 H _ «a ‘ Lee, A “errorlec+ric Generator for Portable louir- \/ ll .- ‘ rent , Electronics, V. 1;, key 1946,1. 196. Lsrk— Horovitz, K., Niifileton, Prooe rties of dermanium ” T-u Power Phys. 13v., V. 69, Stelhen'S , 1"]. 3.31:1 2:5??? erhOf , Contact emf between 1 Reta Rev. V. 69, 1946, p. ’2. V \' ll 1’? Von Lippel, nigh Dielectr 331 Engr. Chem., V. 8, 19 Heller, C., Elec. Rev. V. 49, 1946, p. T H 70 .7 dul, E., E1 h Dielectric Constant he ’333, V. O, No. 6, 1246. loys, II, 1946, p. 259. mpg 50. "Characteristics of Thermon teri ethoj. for 1:91 emiconluct r3, olilrics suring 1hys. Indcs. \JJ rxl ‘\)J r); 44. Gurnv:ce,L.,”Th°r*oelectric Proberties of Conduct- ors”, J. T‘hvs. USSR, v.9, 1945, P. 477, sci V. 10, 1945, P. o . ( In Earlier) Lcwre ce,C.,"This Raiio Runs on Gas , Rao1o Cr: ft Msurer.R.,"Theor. Treatrert of Seniconiuctors and Letgls”,* J. Appl. Phys., V. lo,194E, P.3o3. Seitz, _. ,"Pasic Principles of Semiconductors”, J. .tUnlo 13-3., 0, V016, 19/45,..905530 1944 Guflden,5.,"€lectrical Coniuctivitv of Electronic Semiconductors", Trjebnisse d. .xort. Vatur., 7.13, 1944 , P .23 2'5 . Books Pegder and Warren,”E1ectric Circuits 1nd Fields”, 1943, ‘1cGraw—Till, 13.95. .eo,"Electricity”,1943,Earcourt,?race, and oo., Strong, mlectricll 21 Wineer 11g” ,1943, Kiley, P.74. L.) Periooicals U. ,V.,"A Vote on the Therroelectrorotive 1| Force , Phys. Rev.,V.o4, 1943, P. 37 Meglich,F., and Rompe,:.,"1ectrorh""ic of Solid Fowles”, Cbem.Zentr.,‘ .l, 1943, P.1451 1042 h Periodicals Chilm mr ,J., "Contact Potentials” Phil. “33., 7.3}, 194?, 9 .339 and P. :06. * Not Exec t Title r. .Wifii'g‘hu 47. ‘fl ‘1 \ TI \ 71 ‘ \N “‘5‘: \fl \ )1 | ‘II 0 f—t‘ P-v‘ \ ~ f 7“ ~4- r- i‘A 1-421.?" 1 EFL 1.519LL.P1C 3.1 9314:9121?" l' ‘ '- ;‘ (3 '7: r1 ‘ ‘1‘: __ 937 ’7: , 1."- ’31; r) l :‘Ye .\ tn: 9 nt, 0 O H., ”Else. Confiuctlvlty ?n\ Thermo- ' I "‘ w d” GP Tbs',% Zeits. f. ;ry311:J.119, h) 1;»1 ?fio?2 m A ' Q . “a - "' .fl"‘ r‘ ‘ /‘ JnxTiCLH titute o: :"y: CE, I mner' are, - T ‘ f; -‘r‘ ‘ »‘ r' ‘ (’1 “ ’1‘ ! 1ts hsg1ursm~ 3 ;n1 ortrol 11 SC ience ani - H \ 1 - 1 n Iafivstrv 1941, Reinhold Fubi. Sort. 1. :1. h ‘ ~ ~ . ‘ .' V.‘ '7‘ an: A . 1 h /‘ VOFCCF'Q 943 .LTLZ, L 9V. ung1n13r1nu :Undl“4n— t' 1 v. A - '_ _/L ' 0‘. h 3'2. It -.1L3 -‘—(.;~ 1’ 1'1 -‘Jr ’ t} . - JV . .1. ,,._ n- A 4. . . fl 1 . .fi‘n ‘fi 111beru, ;lfinuPlJlty 231 ywjnct1;m, 1941, ., 1:,4L, 90 1‘49. 7 _‘ v I’fi 7‘. v “A a A ' idlbtgfi, ”., 113~trod -héorj of ner.a:lectr1c .‘+. 4. " T A "A 'f‘y - n v‘r A ' :1 f‘. -f? 3 , L, o (Alfi'fijlo Iflyb 0 V o ’2, l‘J+l, 1). “,J.: 0 pr‘ R H '1. vs .-\ D :3 a V 1'. ' ‘ ‘ ,' Iof-‘ 3., “Sutact 01-:miconuctors w1Ln 1et113, t) 1 :1 'T"**‘ f. _ 1 AI- :Lrn 1.1-1.10 -1C3.io «Co LJJ o, JC’r’ OTIL'rSo 5, l: “:1, :0. _r";\". -1,- A“ ‘- H _ .7‘ . an " .ohldr, 3., VOéenqero on emflera 6? 151rm31 bf]. 43 1941, p. 1-6 Therfia 1 T .1 ‘10 "3‘ and r- 1. ‘.' H , a J - . Beuler, 1., Inxeot1_3tion on the «lsctrlc am ~.~ . . n ,. - 1 Thirmal ghen)M-n3 1n 141’ 19)L~.v , YjA\)d 29. 1020 _4“ HA 1 ,_‘ LZVOL: D H . . v H -. 31, El9ctric1t} and Lagnetism , xcGrzm— v- 1 f“ 1" 21114, 193)), p. /H Jilson, 1., Cng‘ U‘rili C$m96911,A.,”Sim;l9 Demonstration of Peltier .—. r ,.. ,U, H. Affect', Th . soc. ;roc., V. 51, ,99, p. E’; Vua1mvr J., "Ca culat1on of -9lt19r Effect", Cfl.moo Phil. 3020 (T00. V0 35, 1939, p. 521 o fixact Title 67. Kcixnel, J., "Theory of Tr9rmo electric Effects 1.. a I~19:3nctic Fieli', Ann. :1. Phys. V. 3,5 1939, 9. 7O . 69. Schulze, A. , "Letallic Materials for Thermocouples" J. Inst. Fuels, V. 12, March, 1939, p. 941. 69. 5c-'91crert H., eni others, "Thermo-9mf in Metal/ «'1 /. ‘fi r‘ ;eLicon11c tor/retil Elements', V. 34, 1939, .250. I akagi, Y., and Ssto, T., 'Thernoe lectric Power of V, .P‘ " n9 augerlettice Alloy Au Cu , Phys. Hath. Soc., U, V. 5V, 1939, p. 2510 ‘1.“"Q _..-‘12" Books 71. Exrnrell, G.,'T1inciples of Electricity an. Elec- tromzsnetism". 1938 Ncsraw-Hiii, p. 181. 72. Hochberg, E. N., and 30mins k9, M.3., ”3199. Con- ductivity ani Therfioelectric Chlrecteris tics o Semic onjuctors" ,Thys. Z. Sowjet, V. 13, 1938, ;. 198 (lerna 73. Ioehler, J., "Thermojunotions", Phillips Technical Review, June, 1938, p. 165. 74. Kovalenko, V., "Tnermo electric Conversion Effic- iency",* Tech. Phys. -SSR, V. 5, 1933, p.739. 1937 Books ein, "Textboolc of TherUIOiynamics" , 1937, Y: p0 361 76. Hirst, ”Fundamentals of Electricity and: ‘ 1 net- . H ism , 1937, Prentice-1-911. p. 131. q .q K1 ’ijwareux and ”3990, "Principles of Electric and dagnetic Neasurements”, 1937, Prentice-n,ll,1.-4. * Not Exact Title f". 81. 1") \W ‘3 w ~ P T .‘\ , ”t T ’N A - ‘u v w " y p 1 T“ ,"-‘ ,\ motu, -., a“ 333:, 3., “33 LMeor‘ 33 toe -Iug‘ - ‘l - 1 a " A 1 v “w H A f -r » “t‘es of Letalo 2K1 3130; 333, Oufor3. tax—1% F) 4 ('5') 1 (V . :L _.. .J-s .J'_“-LLD H3rtmaun, »., ”El-PtWical In’sstijatiJH of Oxide STUiCOfiJUCtOIS Z9it. f0 Eh'So V0 10?, 1936330709 33333;, 3., an? ioch, 2., ”Tdeor331331 Trogtn°3t o €13 Con‘untivit" 3nd 'herroalectric Torer of 5331— Con :Suotors ,* Zait. f. “P'sik Che3ie, f 3;, 1935, b. 439. 107K ) # I h .5 ‘ ‘ .- 1" -30 0:. E) 'orclivs, C}., "3run.& 133%3A1W18 fetJllj.s<fl13n Zu3- 7 L t1L3es fhycikalische Vi Denschaften" H3ndbuch der mot3llphysik, 1933,0L013315. Yutnhinson, ”Advanced Textbook of Ele1tricit' and Kagnetism”, V. 2, 1935, Univ. Tutorial Preos,p. l3 ‘7 1“ her, 3., ' mloktronen Loitun3 33lvan3m 33net- 3r rmoeleLtr' ache un‘ vAr.3n339 Efcht Panibuct def EXperimontalphysik, Vol.2, 1935,P3rt 7‘15” . ”H1 3 ~ “1 ' z . U E V A w~ 333339;, LLQHQQtS of ALQCtTlCLtJ , 1:3,, “(333.— -3. 1 J \( All. *1— ’ T..7'~4,’O h 1 fl' .1 rerLC- 110 1.1.5 1 L - 1"- A 1" O V“ R.” - —\1 ‘I- —. A A I" ’ o 'H '- v1u0,m., Lebnx Ale 13o33033633rizc3-1 Tgfcnte ',‘ :5 ‘ \3 H‘ W ‘v -. ‘ ~ - ' 1' .‘ ;— A F~r~“~ ‘ L .303 :9? DEucfl Llentroo3tnoor1e , sci-Moe n-'Ofb3, 1,7 “ ‘.' ‘91-: *3 r- $01054, 50V. 1);), ro:?30 1:24 #- L—t .L‘. ~—x : "‘ '\ f. T‘“’“ ‘ “r. 37' Ar \ t A! *11'L . 1 ‘1‘ ‘- or 33 “n, 31c -nor303jl3nioo of 33933r1333 3.3- ~-. _. \i‘fi . “ ‘\ & H r“ ' ‘ , ' .. A 3333.3 1. 393313 , 73%, 330311333 ‘I!-" H r. A D 1“ r-s‘a- I — fi‘fi . 333?, L., Co p138 u; 3333iable i3or.oelectrlc ’3’ " . ~‘ \‘ «A ‘ N “1 ~ I -: 7* ' 'T_ 7'. .039?” , _6Vue 3.33331 del ALCCorLCiU e, Vol-)3, *Yot Exact Title TI) - ll . H (a‘ "I ‘ 1 A: l“ f: n D ' — 7 O .4 '\ -«'L . - ‘u , J—I' . a ’ , 3-; ;rifib.3. exaxt "attrwiss, V01-13, 1§34 v I " 3 ,. q , v 9;. Ewrr*;,I., *Eer1~* actric ”ouvers... ;ff ;iOQCJ" ‘h - A. 3,. 1r .— A I (7:: .A.“\,rl:). Cr. {01043, 1,?“ Do "4‘. A H v0. Jove:,?.,"Tthz:?1=ntrin Co v 7:szq Effici?ncv , ’2‘ TV .—. -"7’ _.r I“) "7 2T. .JCiO -LIQt'TO’V01oll, l;/'L,:‘o'—{‘+l o 1010 - :- 7" ;ooks h 0 ‘1 A. """'1 ‘ v _ ",-\ ‘ O. "» A it’\ >11 I :‘LCi-‘Z’V K190tr‘15‘1t‘f 7111 _‘ A (Twat-218.: , 1k", 3 , IUSLC- ' llama, ’1) 11¢”. .o.l -. 4‘. O J .. . F?rioiiogls "?. Vi“ “fir,7.,”T%~rmnc‘cctrin :DWOP of C‘."L*°.3",“c / c. U - ~_ A.. 5.; - V V 4 Av - ,— , ‘ __‘- *1 n“ .1113. 'fi‘y" 11’ .01015, 1E3-,J-O 1‘45. Q: _54; Book" A "r fl ,v ”m r,- :‘f h H f‘ 53. sums—iothéry,fl., .he metallic .tate , 1:312CXfOTd f4. Leek,"?unM :iehtals of Electricity 211 -3;netism" 1931, *iley, P.166. '1‘ . .- - ”\v H ‘. , ~ A ‘ T H A 53. rafe :nl Aiams, Principlua of T1?ctv1:1tJ , 1931, U.V9n ostroni “0., 3.?19. P7P1031”313 96. Ciil?y,Y.,”The RaspQQS? o? T%?PTOCOP:1?SH, XeCF. T1;r., "1753, 1931, ?.7§7. 1 L r‘ H _y_ \ ’) '\1 }..J‘ H r.) O 13 ‘v ., K H .—. -0 ., 93.w1?er RAJ 3th::rt,Pr1nciploa O ;n;1ne Ti "?.ro:yq