T r
Y
URING the course of preliminary investigations on miscel-
portland cement takes on permanent growth with the successive laneous industrial solids with the electron microscope, wetting and drying over a long period. This growth is accounted unusual crystal forms were observed when a waterfor by the hydration of the inner portion of the cement particle, dispersed sample of portland cement wa$ examined. A review of which was previously protected by the colloidal mass around it. the literature indicated that comparatively few studies of the In 1901 Ambronn ( I ) studied the crystallization of portland hydration of cements had been made by either the light or the cement with a light microscope. During the first few days he electron microscope. Consequently it was decided t o undertake observed t h a t the individual particles of the cement became an electron microscope study of portland cement compounds dissurrounded with a large number of exceedingly fine needles and persed in water over a wide range of setting times. Although hexagonal plates. After a few days a third kind of crystal was the photographs presented in this paper do not give complete developed, also consisting of hexagonal plates. Finally, he reevidence &s t o tlie products of hydration, they do reaffirm certain ported that the presence of air caused the formation of a biscuitof the principles previously laid down and demonstrate the apshaped crystal, which he believed to be calcium carbonate. plicability of the electron microscope t o the study of crystal formation. TECHNIQUE W I T H ELECTRON MICROSCOPE According t o Bogue in 1928 (3), “exact information on the It is considerably more difficult to obtain a sufficiently dischemical nature of the major reactions which accompany the persed layer for observation in the electron microscope by an air setting and hardening of cement has not been advanced materially dispersion of the specimen than by a liquid suspension; hence, in the last quarter century and, indeed, but few contributions the latter method was used in this undertaking. The usual have appeared which would change in any considerable degree dispersion medium is water, although other liquids may be used. the conclusions reached by LeChatelier o n this problem in 1887.” Figures 1 and 2 show samples of portland cement and a neat The theory postulates that portland cement is composed priportland cement pat which were dispersed in petroleum ether; marily of five compounds: tricalcium aluminate, tricalcium in all other instances water was the medium. A small quantity silicate, dicalcium silicate, tetracalcium aluminoferrite, and of the solid-about 0.5 t o 0.75 gram-was mixed with about 10 cc. calcium sulfate. The first four of these constituents hydrate in of freshly boiled, distilled water and allowed t o stand for contact with water, thus remove the dissolved constjtuents from various periods. At all times there was a n excess of solids the solution, and cause more of the initial material t o be disin contact with the liquid. The specimen is dispersed in a solved. By this process the initial material enters the solution thin layer on a collodion film,supported on a 200-mesh stainand forms a crystalline mass, holding together the aggregate and less steel screen 1/8 inch in digiving strength t o the concrete. ameter, for observation in the elecTable I lists the compounds tron microscope. A wire with a and indicates the method of l/S-inch end loop is dipped into h y d r a t i o n g e n e r a l l y accepted C . M. SLIEPCEVICH, L. G I L D A R T , the vial containing the solution, (W, 7). I n addition t o these reAND D. L. K A T 2 and the droplet of liquid clinging actions, hydrolysis reactions have University of Michigan, Ann Arbor, Mich. t o it is transferred t o the film by been reported (3, 4, 7 ) . Tricontact. The water is allowed t o calcium aluminate and tetracalevaporate by standing in a closed cium aluminoferrite are believed dish or desiccator for a few minutes, to be the first t o react and t o and the specimen is then placed in the holder and inserted into the give the initial strength t o the cerrlent. Tricalcium silicate microscope. Most of the micrographs of this paper were taken of reacts next and dicalcium silicate last. These studies were based primarily on chemical analyses and on physical measurements on samples from glass vials which had not been agitated and from what appeared to be the supernatant liquid. Thus, it is possible cement test specimens, such as water absorption. Observations t h a t particles were not present in the liquid, but that crystals obon crystal formation added little t o the theory. Since not enough water is usually present in the hydration served in the microscope resulted from the crystallization during of portland cement t o satisfy all the constituents, the products evaporation. I n some cases the water and sediment in the test of reaction take on colloidal properties. White (8) showed t h a t tube were agitated and a cloudy sample was taken, but most of the 178
November, 1943
INDUSTRIAL AND ENGINEERING CHEMISTRY
An electron microscope study has been made of crystals resulting from t h e hydration of portland cement compounds. Calcium hydroxide yielded spheres and a fibrous mass. The dicalcium silicate hydrate appeared as rhombic slabs and possibly as amorphous spherulites. The tricalcium aluminate hydrated t o form thin hexagonal plates, rhombic slabs,
1179
needles, and possibly amorphous spherulites. The amorphous spherulites could well be *me f o r m of hydrate of both of these compounds, but t h e photographs show t h a t they bear a resemblance t o the known calcium hydroxide. The calcium sulfoaluminate complex formed heavy needles or splines. Amorphous forms of ferrite were also observed.
specimens so ubsarved contained m:rterid too dense for observe The spaces of the 2W-mesb screen were examined, and enuogl, tions to be made. However, wherever these specimens were photogmphs were taken of oach sample t o be representative ofthg observable, na differences in crystal form between agitated and entire field. S p e d c u e wm exercised to avoid dust omtaminsunagitated samples could be detected. It is possible that tion, and frequently blanks, of film and screen done, were obBrownian movement or thormoagitstion maintains in suspension served as B check. the finer particles resulting from the hydration of the compound, In moat of the preparations the water suspensions of p o r t h d and that they were present as actual particles when placed upon cement were immediately stoppered st the time of miring and the swecn. The evaporbtion of the wyRtm naturally leww some were kept sealed until the moment a t which tlle s:bmple WBB solid residue, which either may attach itself to the crystsls SIplaced on the film. Since drying way carried out in a deaircator ready present, may form new crystals, or may give B background containing sods lime for removal of carbon dioxide, the maximum cantsct time of the ssmple with atmospheric carbon dioxide deposit of more or less m o r p h & ? material. Tyndall effect o1,wrvations were made on all eamples. The w n ~about 2 or 3 minutes. The distilled wnter used in the results were negative in all cmes except those of trioalcium preparation of the samples was freshly Soiled each time as aluminate and calcium hydroxide. A8 a check on the &e& 01 further precaution sgeinstcarbondionide absorption. evaporation, it 3 per cent solutioiiof sodium chloride was used to prepare a specimen. Perfect salt cubes were found, as well as some hase in the bsokground. It, thus appears that crystals were TABLE I. S ~ M M AOB' * ~REACTION^ T GWENFOR SETPING OF POXTIAND formed during the evaporation of water on the CEMENT (7) film, but tho possibility that. some small crystals Compound Roeeti"lla may have been present at the time tlie specimen Tiiuaioium duminetu 3CaO.Alfi01+ BHrO --+ 3CaO.Ai.Os.fJH~O was plsced on the collodion film is not excluded. 8CaO.AhO~+ 3CaSO&+zHs0-J. 3CaO.dlr0,.3CaSO..SlH1O When in the microscope the specimen is Tiioaicium siiioste 8CaO,SiO* + r H 1 0 3 2CaO.SiOr.rIirO + Ca(OHh Dioalrium rilieste 2CaO.BiOi + s H . 0 --+ 2CaO.SiOz.zHzO under B reduced prevsum of 10F mm. of Tetrsoelsium slumina- ~ C ~ O . A I I O I . F + E ~rH*O ~ Z 3SCaO.AI~0a.rH~O + Ce(OH)% mercury, which evaoorstes any water not prsierrite .t FB,OS.ZHIO viously vaporized.
Figure 1. Portland Cement A Dispersed in Petroleum Ether and l e f t Standing One Week (X19.000)
Figure 2. Neat Cement ]%I, Ground in Mortar and Dispersed in I'otroleem Ether ( X S W )
Figure J.
Calcium Sulfate Hydrated 18 Hours (X8W)
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I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Voi. 35, No. 11
Figure& Calcium 0xidelfydr.ted 4 Days in a Softation Sntumted with Carbon Dioxide (X13.500) t-
Since ~n excess of liquid (plitced on the collodion film) rfsultod in a specimen which was s h o s t opaque, some care RTS required &s to the quantity deposited. The results of this rtudy include d s t s from a number of observations on specimens which, while not suitable for photographinR, were sufficiently defined for virrusl observation.
Figure
6. OlIoium Iiydmxide Hydrated 18 Hours (X@W
Figure 9. pDiealeium 5ilirnte H y drsted 2 Iinur. ( X 10,SOO)
Figure 7. Cdeium Hydroxide Hydrated 7 Days (XW)
Figure 8. Calcium Hydroxide Hydrated 7 Days and Exposed to Atmosphere for 3 Days (XSOM))
Figure 10. ,%Dirsleium Silicate €lydmtt.d 16 I h v r CX13.500)
Figure 11. 8-DioaIcium Silieate Hydrated 10 Days (X10.500)
PORTLAND CEMENT CONSTITUENTS
Eleotrun mierogmplrs ivero taken of the hydrstitiuu prodwtirom the pure cmtititueuts, artilieid mixtures, and poitlaed cement mixturn. The hydrates of the pure ccnstit,uents will lbc presented first so thet they may be later used in ideirtifyiirg some of the products found in the complex e m e n t mixturer. The snmplea of gypsum, dicalcium silicate, triedeium rilicntc, tricalcium sluminate, snd tetrmalcium dominoferrite were furnished by T. L. Brownyard of the Portlnnd Comerit Associstion. The triceleiwn silicate may contain some dienlrium silicate, and the tricalcium aluminate may contain s o m ~fnr: lime and some materid with II lower &io of lime to alumina than 3. Sinco the dicalcium silicate XIS prepared by using 0.5 per c m t borax BS B flux, it may also be slight.ly eon-
i‘iqure 7 is not identified, but similar structured were found IPiwitedly. This substance might be the result of contamination 1ty cnrhon dioxide, which caused B calcium hydroxide sphere to nwystalliw, or another form of calcium hydroxide resulting from tho preesence of foreign material. Another photograph of tito nilme slide &s Figure 7, but of :m ndj;ioeot field, was like Fimre li. Figure 8 show calcium carbonstel formed by the carbon dioxidp of the sir reacting aitb the sdoiurn hydroxide. The particulrir grouping of the crystals is typicd of the field and would indicntr h 8imiis.r uberrvativns were made by Ksdcsowaki at Y I . (6) for oalciiim hydii,iidc and (or DRIC~UIII carbonate.
tsminetri. The other t w o materi:ds, gypsum and tetrsoalcium aluminofrrritc~.shrmld be essentially pure. C~UICIDM SULFATE. Crystals of upsun, (formed by placing n drop of clear supernatwt solution on B fih srnd nilowing the wutw t,, evaporate) sere observed after vilrious setting times. Figure 3 shows the type of crystals formed, which are independent of the settiny time. This sharp, angular, monoclinic type of structure is eharncteristio and resdily r w n duoible. types ~f cryC u c i u ~ lH ~ o n o x r o ~Three . st& were formed from four different prepfsw tions of these samplca. Calcium oxide sli di.olued in “carbon dioxide free” water, ;trrd the suspension wna &owed to stand for 2 dsys before the slide (Figure 4) was pmpnred from this dispersion; the spheres 81’8 believed to b. eafcium hydroxide’. The slide for Figum 5 wax prepared from B solution of calcium oxide
Figure 14. Tlieslrium Silicaie I t y d r a t e d 10 Days (X13,m)
Figure 15.
Triralcium
Silicate
Hydrated 10 Day8 (XlO,%O)
Figure 16. Triealcium Silicate Hydrated 2 Hours (Xl2,SOO)
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 17. Tricalcium Aluminate Hydrated 2 Hours (X21,OOO)
Figure 20. Tricalcium Aluminate Hydrated 10 Days ( X10,500)
Figure 18. Tricalcium Aluminate Hydrated 18 Hours (X13,500)
Figure 21. Tricalcium Aluminate Hydrated 10 Days (X16,500)
t h a t they were present as such at the time the solution was placed on the field. ~-DICALCXUM SILICATE. The dicalcium silicate is supposed to form one hydrate. Figures 9 and 10 show rhombic slabs adhering in the form of accordion-shaped aggregates. Since these structures closely resembled those of calcium carbonate (Figures 5 and 8), an attempt was made to determine the possibilities of carbon dioxide contamination. Samples of dicalcium silicate and calcium hydroxide were prepared from the same carbonate-free water and were treated in exactly the same manner with the usual precautions taken against carbon dioxide c o n t a m i n d o n . The calcium hydroxide specimen showed the typical spherulites of lime hydrate, and there were no signs of
Vol. 35, No. 11
Figure 19. Tricalcium Aluminate Hydrated 18 Hours ( X 13,000)
Figure 22. Tricalcium Aluminate Hydrated 10 Days and Agitated Constantly (X8OOO)
carbon dioxide contamination. Had any carbon dioxide been present, the lime would have been converted to the carbonate form of Figures 5 and 8. Consequently, it was assumed t h a t the dicalcium silicate sample was likewise carbonate-free, and therefore the rhombic slabs were some form of dicalcium silicate hydrate. Furthermore, since the figures presented are in all cases representative of the entire field observed, i t seems unlikely t h a t sufficient carbon dioxide could contact the specimen and convert all the dicalciub silicate t o the carbonate form. On the other hand, Figure 11 resembles the usual hydration product of dicalcium silicate as revealed by the light microscope. However, this type of structure wa3 obsewed only after hydration periods
November, 1943
I N D U S T R I A L AND E N G I N E E R I N G C H E M I S T R Y
1183
is compiii&ie with t.he ciileililn hydroxide uf Figure 6. Figure 16 is the only mtrteiinl found aFter 2-hour hydration. The large pastirk may be the orixind miitt?risl, while the fine maSs resembles calcium hydroxide or a form of dicaleium silicate.
Figure 23. Tetracdoium Aluminofedte Hydrated 3 Fiours in B Stoppered Vial (XZZSO)
The sppilmaca of rhombic slabs in shorter hydration periods remains uiioapleinsble on the basis of existing knowledge, e8peeiall)since dicslcium silicate is believed not to undelergo hydration for several d w r . Therefore, in Ihe light of tliesr ohserv:itions it seems that dicalciilm siliwte may first undergo some intelmedintr reaction Lo form the rliombic struct,uw of Figures 9 and 10. ’hrcnrmrm SILIC*TC. Tliir compound reacts wit,li water to form di. calcium silicate and ealeium hydroxide. Figure 12 gives the spheres of cnleiurn irydroxido and the rhombic slab8 similnr to thoso formed from didcium iiilicnk Fisure 13 &ivm the fibrous material of tho type found in tho c d e i u m hydruxide of Figure 7. Piwro 14 &gainshows tho neeordion aggregations and porisibly either caleiuni hydroxide or a form of dienlcium silicate hydrate similar to tirnt observed in Pigore I I . Figure I:,
TRICALC~UM ALUMINATE.Figures 17 through 21 give the produats of reaction from triedcium 8,Iuminate after hydration hes progresmd From 30 minutes to 10 days. The thin hexilgonal plates of Figure 17 resemble knolin and am probably an unstable form of trioaloium duminale hydrate. Figure 18 could not be duplicated, even after several attcmpts; the needles may also repreaent another unstsble form. However, Figure 19 does contain splines and rhombic erystnls. These micrographs reedily slmv that four types of crystsla may be found-namely, tho hexagonal plates of Figure 17, the needles or splines of 18, the rhombic slabs of 20, and the spherulites of 18 and 20. The spheres of Figure 20 may represent either an impurity of calcium hydroxide, B mult of hydrolysis, or even some form of 8 tricalcium alumimte hydrste. Figure 21 w3s obtained after 10day hydrntion m d bears a slight resemblanoc to oaleium hydroxide, aithou~hthey well might be some form of tricalcium slumirratr! hydint,e. Keiwrmann (S) called the hexagonal pintea “tricalcum sluminate hydrate” and the hexagonal cryst& “calcium hydroxide”. On the othor hand, Ambronn ( I ) failed to identify the line needles and hexagonal plrttes n,hich appeand after contact with water for yr few days. However, both Ambronn and Read (6) claimed that the lwge hexagons1 plates which sppeared after mveveral days were cslcium hydroxide. Figure 22 combines the unintelligible portion of Figure 20 wit.!, the hexagonal plate of Figure 17. This specimen WBS prepared from a suepension that wna constantly agitated for 10 dlrya. The investigations show that triealoium aluminate containing possible impurities of free lime and mono- or diedcium sluminate, when dispersed in wster, yield hexegonal plrttes, needles, aecordion?shaped aggregations of rhombic slabs, and spherulites. TETRICAKIUN ALUMINOPERILITE. This compound i s believed to reaet with water to form tricaleium aluminate, calcium hydroxide, and some form of ferrite. Figure 23 represents an unusual long+hain struetore, the elements of which am perforated with lienagonal holes. Figure 24 shows stabs, previously observed in triealeium aluminate (Figure 20) and a background,
of 10 day8 or lungor.
Figure 21.. l’etrscalrium Alurnino- Figure 25. Tetracalcium Aluminoferrite Hydrated I B Hours (X10,500) ferrite Hydrated 10 Days (X13.500)
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 26. Tcicalcium Aluminate (4 Perts) and Calcium Sulfate (1 Pert) Hydrated IO Days (XSOOO)
Figure 29.
Portland Cement A Hydrated One Week (X16.540)
F i p w 27. Tetracalcium Alunrinoferrite (3 parts) and Calcium Sulfate(1part)Hydrated lODays(X6HM)
Figure 30. Portland Cement A Hydrated One Week (XI2,SOO)
Vol. 3S, No. 11
Figure 28. Portland Cement A Hydrated 30 Minutes (Xl6.500)
Figure 31. Portland Cement A Hydrated 18 Days (X16.500)
which is probably composed of ferrite. Figure 25 gi\ies the rhombic dab8 along with a structure rrsombling the calcium hydroxide of Figure 20. If tricalcium aluminate is a product of the re setion between water snd tetracalcium aluminoferrite, then the m e crystal4 should be formed upon hydration of either of these substances. As a matter of fact, even hexagonal pletes s i m i h t o those of Figure 17 hsvs been found in samples of tetracalcium aluminoferrite. However, the chainlike structure of Figure 23 is typioal only of tetraoaloium aluminoferrite; the needles of Figure 18 sre of the tricalcium aluminate sampla.
persion of 3 parts of tetracalcium dumiiiofcrrite and 1 part of calcium sulfate was slso prepared. The results of these hydrations am shown in Figures 26 and 27. Again, rhombio slabs, hexagonal plates, and spheres are found, aj well as splines, which form a network over the slide. Judging from the results of the investigations on the pure constituents, it is obvious thet the heavy needles or splines m e B cnlcium sulfoaluminete oomplex. During the eerly stages of this investigation T. L. Brownyard suggested that the heavy splines of micrograph 111, Figure 32, could possibly be the odoium sulfoaluminste, 3CsO.Al&. 3CaS06.31H20.
MIXTURES OF COMPOUNDS
PORTLAND CEMENTS
Sinue calcium sulfate is held to enter the reaction and retard the set of portlsnd cement, s swpension of four psrts of tricalcium sluminate and one part of calcium sulfate by weight wss studied in an attempt to verify this theory. A similar dis-
Since the constituonts described compose port.land cement, the electron micrographs of films prepared from solutions of the cement should confirm t.he observations presented. Two cementa were examined: A is a normnl, commercial portland
November, 1943
INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 32.
Portland Cement A Hydrated 18 Dirp I, Xrsm, 11, x9m1 111, X Z O . ~ .
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i 186
INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 33.
Portland Cement B (Sample 3) lirdrsted 24 Hour* in Stoppered Vial (XZ2501
Voi. 35, No. 11
3. Although cnleiuni hydroxide gives &teres 8s its principal product, a fibrous UP needlelike 8truoture is also often observed. 4. Calcium oerbonate forms rhombic dabs which d h w e to one mother aa judged by the products of carbonation of calcium hydroxide. 5. Dicaleium silicate initially hydretcs to rhombic slabs which adhere to form accordionshaped aggregates. I ~ t e r ,amorphous spherulites are found. 6. Trienleium silicate hydrates to form the same products i k ~diealeium silicate in addition to esleiuni hydroxide. 7. l’riealcium iiluminste, which may contain small amounts of the mono- or dicaloium e m pound and lime, give8 rhombic slnbs, thin hexagonal plates which resemhle kaolin, and spheiulites. In several iristames rioedles and splines hsvc been observed, but sulfate contamination could pofisibly have accounted for this third type of cryst$. 8. Tetrnealcium duminoierrite deeomposoa after several hours to form the =me products BS triedeium aluminate. plw a backmound of ferrite and possibly calcium hydroxide. The 3-hour hydration sample gives a unique unstable chain structure not found in any other spenimen. 9. Mixtures oi gypsum with tricelcium aluminate and with tetracalcium aluminoferrite produce heavy splines. Some fraetunx of theso splines indicate that they may be hollow with fibrous wslls. 10. Both dieelcium silicate and tricaloium aluminate hydrolyze or change after several days of hydration in a. rcletively large quantity of water to yield spherulites which sppear similar to calcium hydroxide. 11. Although calcium carbonate, dicirlcium si& csto hydrate, and one product of hydration of the
cement of unknown composition; LI wti furniviied by A. N. White, and has the following oomposition [in per cent by weight): SiOn AKJl
SerOl
21.55
s:o9 2.66
CaO MeO
so2
63 01 2.18 0.00
T h e suvpensions of cement A were expo& to atmospheric carbon dioxide; those of cement R were weU protected from the atmosphere in stoppered vials. Figure 28 is e, typical field of cement A after hydration for 30 minutes before the film W H . ~ prepsred. Figures 29 and 30 itre succewive micrographs of B layer prepared from cement A, whioh had been hydrated 7 days sild exposed to the atmosphere; Figure 31 ia a sample which had been hydrated 18 days in oontact with air. Figure 32 illustrates the effect of B combination of ineresued magnificatioo and phot+ graphio enlargement on the same field. Cement R gave similar photographs to cement A. Figure 33 i s b series of micrographs following the length of a spline (0.0023 inch). Figure 34 shows the cffect of 7-day hydr;ition. Figures 28 and 30 are believed t o be original pwticlea o f cement girded with the hydration products. SUMMARY AND CONCLUSIONS
1. Crystals, formed by hydration and tiydrolytais of portland
cement compounds in water with subsequent evaporation of the water during proparation of the specimen, have b a n examined with the electron microscope. 2. Gypaum forms monoclinic type crystals in nU CLIS~S.
Figure 34. Portland Cement R Hydrated 7 Days (X20,OOO)
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INDUSTRIAL AND ENGINEERING CHEMISTRY
tricalcium aluminate all form similar rhombic slabs, the authors believe them to be separate crystals. 12. With the possible exception of gypsum and the thin hexagonal plates formed from the tricalcium aluminate sample, portland cements show all, but no more, crystal forms than those which have been observed from the pure compounds or mixtures. 13. The crystallization taking place in this research may be somewhat different from t h a t when a minimum of water is present and the material is gelatinous. However, when considered on the basis of phase equilibrium, the specimens used here always contained an excess of the original material t o keep the solution saturated. Crystallization is likely t o come from a saturated solution, and therefore the equilibrium phases should be identical regardless of whether an excess of water is present or whether they are only partially hydrated as a result of the smaller quantity of water used t o dissolve the original material. However, the wide dispersion of the samples required in order t o observe crystal structure made the dilute dispersion necessary for this study. 14. The 36 electron micrographs presented were selected as representative of more than 250 photographs taken. Approximately a thousand visual observations were also considered in assembling the data. 15. Under the conditions of these experiments all substances show crystalline or geometric shapes except the deposit of ferrite and the material resembling calcium hydroxide. The amorphous material formed from tricalcium silicate, dicalcium silicate, and tricalcium aluminate, after long periods, resemble calcium hydroxide but could be colloidal forms of thq silicate and aluminate. If these spherulites are the final form of dicalcium silicate and tricalcium aluminate, the colloidal theory becomes more plausible. However, in t h a t case the hydrate of tricalcium aluminate should be written with a variable water content rather than with 6 molecules of water.
1187
16. If these results can be correlated with portland cement reactions occurring in ordinary industrial proportions of water to cement, i t may safely be concluded that the strength of the concrete is attributable t o an abundance of crystals in the form of splines, needles, and fibers matted together and bonded by the amorphous mass. Further, strength may be imparted by laminations and the strong surface forces of numerous thin platelike crystals. ACKNOWLEDGMENT
This research was made possible by a grant-in-aid from the Horace H. Rackham Fund. 0. S. Duffendack of the Physics Department, under whose supervision the instrument was operated, made valuable suggestions. T. L. Brownyard of the Portland Cement Association furnished the pure compounds, A. H. White, of the University of Michigan, furnished cement B and made helpful suggestions. Suggestions also were received from several individuals, including L. S. Ramsdell, G. G. Brown, and L. Thomassen. G. Sawyer, K. Beu, L. Kavanau, and P. Barker were student assistants. LITERATURE C I T E D
(1) Ambronn, H.J., J. SOC. Chem. I d . , 28,366 (1909). (2) Bogue, R. H.,“Digest of Literature on Nature of Setting and Hardening Processes in Portland Cement”, Rock Products,
May to Sept., 1928, inclusive. (3) Keisermann, S., J. SOC.Chem. Ind., 29, 1339, 1383 (1910). (4) Leighou, R. B., “Chemistry of Engineering Materials”, New York, McGraw-Hill Book Co., 1931. (5) Radczewski, 0.E., Muller, H. O., and Eitel, W., Zement, 28, 6937 (1939); Zentr. Mineral., Geol., 1940A,4-19. (6) Read, E. J., J. SOC. Chenz. Ind., 29, 735 (1910). (7) White, A. H., “Engineering Materials”, New York, McGrawHill Book Co.,1939. (8) White, A. H., and Kemp, H. S., Proc. Am. SOC.Testing Materials, 42, 727 (1942).
Nomograph of Dittus-Boelter Equation CHARLES J. RYANT, JR. Standard Oil Company (Ind.), Whiting, Ind.
A
CCORDING t o Jakob (I) the following equation represents the best practical expression for predicting the heat transfer coefficient of a substance in turbulent flow inside smooth pipe:
SYSTEM OF MIXEDUNITS
Symbol p
k C, p
This expression is a familiar form of the Dittus-Boelter equation and has been experimentally checked for many liquids and gases (1). Although this form was proposed by Nusselt, i t is usually known a s the Dittus-Boelter equation because of the outstanding work they did i n evaluating t h e coefficients and exponents. McAdams discussed t h e various expressions advanced by different workers i n this field and their meanings (9). Often workers shun the use of this rather handy tool because it is necessary t o use consistent units, which are seldom found i n experimental reports. This, then, entails the use of conversion factors, and i t is not uncommon for engineers t o misplace a decimal place in the procedure or neglect to use the proper conversion. To remedy the situation, a nomograph of the Dittus-Boelter equation has been prepared and corrected so i t will be satisfied when the following system of mixed units are employed:
u
D h
Definition Density Thermal conductivity Thermal capacity (numerically equal to sp. heat) Viscosity Linear velocity Charaoteristic length (diam. for round tubes) Coefficient of heat transfer
Unit Lb./cu. ft. B . t. u./(hr.) (ft.) (” F.),
B. t. u./(lb.) (” F.) Centipoise Ft./sec. Inch B. t. u,/(lir.) (sq. ft.) (” F.)
Consider the following example: A wnterlike substance (density 60 pounds/cubic foot, specific heat 1.00) is flowing through 1-inch i. d. tubes at a velocity of 8 feet/second. If the viscosity of the substance is 0.4 centipoise and the thermal conductivity is 0.4 B. t. u./(hour) (foot) (” E”.); what heat transfer coefficient should be used i n calculating the over-all coefficient? Analysis of the problem shows i t t o be simply, what is h when p , k , C,,p, u, and D are given? T o obtain h, lightly indicate on the nomograph the values of p , k, C,, p, u,and D given in the problem, on the proper axis. These
