C o ~ c n ~Corxrur~a m hrr
AND
UTII,I-PY. RUENA VISTA D n x v ~AND BRIOOE, RIVERSIDE, CALIF. .
.
I
Ef'fect of Composition of Portland Cement on Heat Evolved during Hardening HUBERTWOODS,HAROLD €1.SrEiNOwR, AND HOWARD It.STAHKE, Riverside Cement Company, Riverside, Calif. HIS paper presents a study of the heat evolution during
'I'
THEOILY OB DETERMINATION OB' HEATEVoI.ETloN the hardening of Portland cements of varied composition. Heat of hardening is here defined as the tot.al The amounts of heat evolved by the hardening cement quantity of heat evolved from the time of addition of the prastes, from the time of mixing up to the time of test, were degaging watcr, until the end oft.he periods for which it is given. termined indirectly from the heats of solution of the various This property is of interest in tho const.ruction of massive samples in an acid solvent (10). aorhs such as dams, in whicir the great thicknesses severely This determination is based on Ifess's law of constant heat summation (7): The change hinder the outflow of the heat. in heat content of a system in The consequent rise in temTh8 heat evolved during setting and hurdening passing from one state to anperature while tlie cement is has hen determined at 3, 7 , 28, 90, and 180 days other is independent of the path hardening may result in conwhereby the passage is made. tractions and cracking when .for a number of Portland cements of varied coniAs applied to the present the event.unl cooling to the posilion. The cem.en.ls ure mixed neat with 40 work, this method requires a surrounding temperature takes per cent (8 ualer, and are stored at 35' C. determination of (1) the heat of place. (95'' F.) in sealed bottles. Ifeat liberation is desolution of the cement in its iniThe compositions of the cetermined br the heat of solution method. The retial state (that is, unreacted), ments prepared for this work ( 2 ) the heats of solution of were varied over a wide rauge sults are analyzed by the method of least squares the cement after rraction with with a view to bringing out the for the contribution .f each per c m t of each comwater for various lengths of essential fact,ors governirrp heat pound to fhe total heat edution on the assumption time, and (3) the difference beex-olution. that there exists a linear relationship between the tween the two quantities to T h o heat evolutions were decornpound composilion of a cement and ils heat obtain the value of the heat termined over various intervals evolved on hardening. of time up to 180 days, using for evolution. The componnds comprised in this this purpose samples of neat arwlysis ure lricalciunz aluminate (3CaO.AlzO,), cement ma.de up to a water conCALORIMETZR DESIGN tricalciurn silicate (3Ca0.Si02), tetracalcium tent of 40 Der cent of tire rrriaht aluminoferrite (4CiiO~Alz03~Fe20,), and p-diof cement; and stored a t 35' C. The heats of solution of the calcium silicate (ZCuO-SO,). vnrious samples were deter(95'F.).
1207
INDUSTRIAL AND ENGINEERING CHEMISTRY
1208
mined in a calorimeter designed especially for this purpose. The calorimeter, shown in Figure 1, is composed of the following essential elements: A cylindrical copper vessel of about 1200 ml. capacity, lined with pure gold, and chromium plated and olished on the outside. A tight-fitting cover for the above vessey, which cover is plated and polished on top and covered with Bakelite varnish on its lower surface.
Vol. 24, No. 11
The primary purpose of the heater is to permit a determination of the effective heat capacity of the reaction vessel and contents. It also serves as a means of temperature adjustment upwards to the desired value before commencing a determination of heat of solution. A bank of storage cells, a potentiometer, galvanometer, standard cell, volt box, and standard resistance comprise the energy source and means of measuring the energy input to the calorimeter. All temperature changes were measured with Beckmann thermometers carefully compared with one calibrated by the Bureau of Standards. After setting up the calorimeter, it was submerged completely, except for the upper parts of the chimneys, in a water thermostat controlled automatically to *0.003° C. Temperatures of this water bath were observed frequently during each run. Time intervals during calibration runs, and during the rapid rise part of a determination of heat of solution, were measured on a chronograph. Where the rate of temperature change was low, as before and after the rapid rise due to addition of the sample, time intervals were measured by a watch. The solvent used throughout this investigation, adopted after a number of experiments, was an aqueous solution of 2 N nitric acid and 0.25 N hydrofluoric acid.
PREPARATION OF CLINKERS
I.
FIGURE
CALORIMETER A cylindrical brass outer jacket completely surrounding the inner reaction vessel just described, chromium plated and polished inside, and fitted with a removable water-tight cover. This cover is fitted with several chimneys, as follows: One admits the stem of a Beckmann thermometer, which passes also through a gasketed opening in the lid of the reaction vessel and into the liquid therein. Another contains two ball bearings holding a shaft for the purpose of driving a propeller stirrer in the inner vessel. A third chimney admits the stem of a funnel through which the powdered sample is introduced. A fourth carries insulated wires leading to the heater coil described below. An electrical heating coil of about 50 ohms resistance, sealed between two brass tubes which surround the propeller stirrer and serve to direct the circulation. The entire heater unit is mounted vertically by three brass legs whose upper ends are fastened to the lid of the reaction vessel. The wires leading to the heater element pass out through one of these legs. The entire heater element is protected from attack by acid by a well-baked coating of Bakelite varnish.
Raw mixtures were prepared by adding to portions of a finely ground commercial kiln feed such quantities of ground technical oxides and carbonates as would bring the compositions to the desired values (6). The mixtures were made homogeneous by rolling on a cloth and by milling in a small laboratory batch mill until the fineness was such that over 92 per cent would pass the 200-mesh sieve. Each mixture was pugged with sufficient water to give a reasonably plastic mass, formed into bars, and thoroughly dried a t about 120" C. The dried bars were stacked checkerwork fashion in a gasfired down-draft stationary furnace especially designed to maintain a uniform temperature. The temperature of each charge during firing was frequently observed by means of an optical pyrometer which was sighted on the charge through a hole in the furnace wall. The temperatures were maintained a t the desired values within * 15' C. The temperatures chosen for firing were determined from tests in a small gas-fired muffle furnace. For each composition there was thus determined the temperature a t which combination of the lime was practically complete (4, 5 ) , and this information was used as a guide in choosing proper firing temperatures for the large furnace. In all cases the total firing time was 3 hours. One hour was
TABLE I. RESULTS O F EXPERIMENTS CLINKER
TEMP.
DURINQ
CmhiaNT
-CLINKER
BURN
SiOt
OC.4
%
ANALYSISA1208 Fez03 MgO CaO
%
%
%
%
-CLINKER COMPOUNDSCALCD. CEMENT SP. INITIAL HEATOF HARDENINQ NEATCEMEXT 4Ca0WITH 40% W A T E R b A h o r - 3 C a 0 - 2CaO- 3CaO.- GYPSUMSUR- H E A TOF Fez08 All08 Si02 Si02 ADDED FACE SOLN. 3 days 7 days 28 days 90 days 180 days Sq. em./ % % % % % g. Cal./g. -Calories per gram6 7 60 26 3.2 1390 588.7 51.2 53.1 72.5 81.2 78.5 15 1 52 29 3.2 1450 575.7 40.6 45.7 61.0 71.9 74.3 S 11 20 56 3.2 1470 623.6 74.8 84.7 9 2 . 2 100.6 104.3 8 11 47 31 3.2 1480 595.5 53.2 63.1 73.7 77.7 87.6 6 7 33 52 3.2 1500 604.5 71.9 78.8 88.8 92.6 95.9 77.5c 9 0 . 3 101.0 103.7 109.2 1530 618.8 9 11 22 55 3.2 9 7 . 7 103.3 108.0 91.5 73.3 611.6 55 4.3 22 9 11 9 6 . 3 1 0 4 . 1 110.2 91.5 79.1 623.0 3.2d 55 11 22 9 92.4 100.5 102.7 77.3 87.5 610.0 1560 3.2 17 71 3 6 72.5 61.5 70.0 42.1 46.8 573.0 1570 22 31 3.2 44 1 93.1 90.1 85.8 77.9 64.7 599.0 1580 54 22 3.2 2 18 9 6 . 6 108.8 114.1 115.9 89.5 3.2 1540 633.4 4 21 26 47 9 5 . 2 106.4 108.7 114.0 611.1 90.6 6.5 1600 47 4 21 26 78.1 83.8 62.8 74.2 585.9 58.8 3.2 1620 34 40 1 23 9 4 . 5 103.7 107.5 113.3 84.8 625.6 1630 3.2 9 12 66 11 91.3 99.9 106.2 109.4 84.0 3.2 1670 624.0 12 68 8 10 49.8 36.3 28.3 564.7 1530 3.2 17 1 61 18
2122 1400 27.7 3.8 2.0 2.5 65.0 2123 1400 26.0 3.5 5.1 2.3 63.1 2092 1440 21.9 5.7 2.8 5.0 65.0 2088 1400 24.6 5.8 2.8 2.4 64.2 2096 1450 25.0 3.9 2.1 2.4 66.6 2085 1400 22.3 6.2 2.8 2.4 66.5 22.3 2086 1400 6.2 2.8 2.4 66.5 6.2 2087 1400 22.3 2.8 2.4 66.5 2094 1500 20.9 5.7 2.1 66.3 4.6 2124 1400 23.5 62.0 7.2 2.2 4.8 2089 1400 22.0 2.3 64.1 4.6 6.1 2090 1400 21.4 66.6 8.8 1 . 2 2.5 2093 1400 21.4 66.6 1.2 2.6 8.8 2125 22.5 62.7 1400 7.5 2.2 5.0 2095 1400 21.3 67.0 2.9 2.6 6.1 2091 1500 21.9 67.7 2.7 2.4 5.6 2170 1400 61.0 2.1 25.7 6.1 4.1 a f15' C. b At 35O C. (95' F , ) . C Average value two tests. d Added as gypsbm and converted t o plaster of Paris by heating at maximum temperature of 150° C. after milling (determined by loss of weight).
..
...
..
1 N 1) U S T 1% I A I,
,Iro\ernt>er,19JZ
A
Y 0 E N ti 1 h' E E 1% I
taken to liring tlie cliarge up to tile desired teinpcrature, and this temperature was then maintaiiied for 2 Iioors. At tlre end of the run the fire was slmt off, and the furritrce and cliarge allowed to cool overnight.. The clinker was removed froin the furnaae, crualied, and ground in a disk pulverizer to approximately -20 mesh. A sample was taken for analysis after thorough rolling, and the remainder was stored in tightly eloed cans.
I'HEPABATION
OF
NG
C €1E M 1 S T t< Y
1209
some degree the lieat evolution, tliere is reason to believe that the conclusions liere reached are generally valid. ~)ETERMINATION Oh. H E A T OF SOLUTION
A t tlie ciid o i the required curing period, one of the vials was reimived from the constant-temperature cabinet, the glass was broken of'i tlie hardened cement, and the latter broken up and ground ai; rapidly as possible in a mortar to a fineness
~ u r ht" h. a. tl" 2 1 1 t".._ ho """.. -..
material would pass a 100-mesh sieve.
CEMENTS
Tlie clinhers pre nared as desclibcd The bottle wnd con-
wit11 amounts of fine
sultiire cements
(PX-
I
--
F i n e n e s s e s were COXCIIETE BRIOGE 1immn Cons~anmron in the calorimeter; a determined on a 200second sample (about mesli sieve. IIowe da weighed piiatinum crucible for deterever, previous work doiie iicrc itus S/IU\YII that equality of 3 grams) ~ a s ~ p l a c in Gneness as measured by a gim!n sieve is 110 proper 1:riteriOn of minat.ion of loss on ignition. Birrce these ground materials equality of effective fineness for cements of varied composition tend to lose weiglit rapidly, the weiglit of the original weighing and physical characteristics, even alien the samc mill and bottle and contents was determined after removal of each of grinding media are used througliout. A lictter measure of the two samples. The smaller sample was kept a t about 900' C. in an eleceffective fineness is the specific suriace~~~~tliat is, t,lie total suri:m of all tlie particles in unit weight of cement. 'The spe- tric muffleovernight, and was cooled and weighed tlic follon~cific surfaces of all the cements produced i n this irivcstigation ing dny. This long ignition period was found necessary. were determined by mceiirs of ii ,sedimeiitationdevicc deucloperl Tlic larger sariiple was dissol\ed in tlie calorimeter, and its heat of solution calculated from the observed temperature at this laboratory (.I) rise, corrected for all signifimnt Ircat tsansferv during t,lie experinierit (9). Tlic liea,ts of solution of tlie dry cenient,s BEPA PARA TI ON AND &PORAGE OX' CZ>I$K~ I'ASTKS were det,ermincd in an analogous manner. TLiree h u d r e d grnms of ceiiieiit and 120 ml. of distilled ~XPEHI\IENl.AL DATA O U V l l N E D \rater were mixed togethcr :urd stirred vigorously for sevcral mimites by a high-speed nrotor-driwi stirper, st the end of The esaeiitial data are given in Table I. Each raw mixture wliich tinre the paste was put into ten glass vials. Tlie vials liad ticen proportioned to produce a clinker of defiiiite compowere immediately stoppered witli corks and sealed with parsf- sition, but,, inasmuch as there were small differences between fin wax. All ten vials were tlien placed in a constant-tem- tire esiiinatcd analyses and those found experimentally, it is pemture cabinet maintained at 3.5" C. (95' P.) where they the latter which mre rnade the basis of further study and remained until required for heat of solution dekrmination. which are report,ed in the table. The storage temperature of 35" C. approximetes the average The clinker compounds were calculated in accordance with mean temperature of mass concrete during the early part. of its tlie findings of I3ogue and his staff (1). The amount of free existence. lime left in the clinkcrs after firing was zero in all cases exValid criticism may be directed a t the time-temjreraturc cept one. 111this case (cement 2095) the amount was 0.03 lristory clioseii for curing the liardening cements, on tlie per cent, a negligible quantity. 9 study of the figures in ground that actual massive concrete structures do not remain Table I shows the following wide ranges in calculated eoma t constant temperature, hut vary, first upward (fairly rap- pound composition: idly) and later downward ( u s u a l l ~less ~ raijidly). However, the same type of criticism could be directed a t any arbitrary time-temperature history which might be chosen. The actual time-temperature liistory of a concrete structure depends on a large number of factors other than the nature of tlie cement. All of the compositions, except that of cement 2092, were The mixture proportions, the ratio of water to cement, the specific lieat of the aggregate, the size and sliape of tlie struc- desigmed to have 2.5 per cent magnesia. Their variations, ture, the manner and rate of construction--all have decided with this one exception, are only such as were occasioned by influenceon the actual time-temperature history. IIence any the experimcntnl and analytical errors. The value was arbitrarily ehoxn curing temperature or temperature history doubled in tlie case or cement 2092 in order to obtain an indecould be criticized as applying strictly only to a small propor- pendent indication of the effect of this oxide by comparison tion of the structures in connection with which heat data with cement 2085 which was designed to be of the same proportional cornposition in everything else. According to might be of interest. While the temperature history undoubtedly influences in Bogue, the magnesia remains essentially uneombmed.
1210
1 N U U S'r I1 1 A I.
A N D E N G I N I3 E W I N G C H E M 1 S T R Y
Heat data are reported for ages up to 6 months. It is planned to contiuue the study and obtain data at 1 and 2 years as the specimens attain these ages. All cements were prepared by grinding with the same amount of gypsum, with the exception of samples 2086,2087, and 2093. The former two were prepared from the same clinker as was cement 2085 and show, respectively, by comparison with it the effect of a larger amount of ground-in gypsum and of alteration of gypsum to plaster of Paris, a change which must. occur to some exteut in much commercial praotice because of the temperatures which the mills often reach. Cement 2093 is a part of cement 2090 to which further gypsum was added in an attempt to improve its setting prop-
expected. The following results of check determinations of initial heats of solution support the estimated calorimetric accuracy: CaMSHT
Col.iomm ,. 623.4-624.1 ~
G10.lLG11.7
2096
603.2-004.5
There are other chances for fortuitous variation in the heat rlnantities than those which reside in the calorimeter and its operation. These may occur in the preparation and curing of the cement pastes and in their preparation for admission to the calorimetar. An indication of the probable over-all error in the heat quantities is afforded by the following data on two cements; each of these was used for the preparation of two batches of cement paste which were prepared at different times and thus had their curing schedules and dates for test displared with respect to each other: 3days
208s 2080
erties. The mixing was eSfeeted i,y additional milling, usiug solid rubber balls which have negligible grinding actioii. In spite of the increase in retarder the cement remained very quick-setting, and partially set dnring the preparation of the paste, as had sample 2090. 13ecause of the laboratory inethod of preparation, all of these cements gave less residue on the 200-mesh screen than is generally tlie case with commercial cements of the same specific surfaces. This residue WRY in all cases less than one per cent. The surface valnes correspond to good rominer&al practice. A moderate range rcsulted from the milling schedule which was euiployed. The snrface analysis is considercd to be reproducible to about * 1.5 per cent; larger divergences were probably caused for the most part by the lack of a scnsitive control over the operation of the preliminary pulverizer. Also, the differences in chemical composition probably liad some effect upon the facility of grinding. The initial heats of solution are those which were olitained with the unreacted cement. The heats of solution obtained with the reacted cement a t the various ages were, thus, these values minus the quantities which are reported as heat of hardening and which were obtained by the reverse calculation.
INETIA~.H a m o* Sornnar
2092 2094
CEMENT
Los A N ~ E L ECor.rs~brr ~ UNDER CONSTRUCTXON
Vol. 24. No. I 1
HEATOP Hhsarniwo 7days 28 days Y0da)a calorie* psr *rGm 90.3 101.0 103.7 88.8 101.7 104 6
!%!
!18:$
108.3 105.0
-
180dsye
109.2
107.0 108.0 104.8
A elrech of t.lie heat of solution method itself m w made using a sample of ceinerit 2094 which had been subjected to further grinding with the idea of causing it to liberate its heat more rapidly. A paste was made up and poured into a bottle which was then placed in water in the calorimeter vessel. The calorimeter was assembled and placed in the thermostat, and the temperature rise was followed on the I3cckmann thermometer for 12 hours. Aftcr this period the specimen was taken out and ground, and the heat of solution determined in the usual way. Seventeen minutes intervened between the mixing of the paste and the first reading taken after assembly of the calorimeter; but the initial temperatures of tlie materials and of the water in the calorimeter had beeu taken, and this enabled the heat liberation during this initial 17-minute period to be calculated on the assumption of negligible loss. The heat liberated during the time (45 minutes) required in pre'eparatinn for t,he final heat of solution test was estimated by extrapolation of the timetemperature curve. Thus the heat of hardening over the half-day period was calculated from the temperature rise occasioned by the specimen during that time and corrected for heat transfer between calorimeter and bath; and, using the same specimen, the value was also determined by the heat of solution method. The results compare as follows: ML-nrOD
IrsnT UI EnsoENlNa Cal./WG7Il
H e s t of solution Diraot temperstare rise
38.8 86.4
The agreement is Considered to be good, especially in view d the nature of the corrections which the direct method required. The outcome of this experiment is in confirmation of
the assumption that the clear solutions which are obtained with the cement powder, and with the hardened pastes prepared from it, are really in the same state, which the validity I'RECISION OF DATA of the method demands. Further confirmation is seen in the The calorimeter was designed and operated to obtain for :L vcry reasonable time sequence of heat valuuea obtained for each directly determined heat quantity involving a 3" C. tempera- cement (presented in Table I). Only cement 2122 shows i~ ture rise-a precision represented by a prohalrle error of about regression a t one age, and it is within a reasonable cxperi0.1 per cent; this would thus correspond to a probable error mental error. If colloidal solutions had been obtained which of about 1.5 per cent for a heat of hardening (obtained by strongly affected the heat values, it is believed that a more difference) chat was roughly one-tenth of the magnitude of the erratic behavior mould have resulted. Examination of Table I shows that the most rapid evolution initial heat of solution. Actually the temperature rises were somewhat less than 3" C., so an error of perhaps 1.5 calories of heat occum during the first 3 days, and that after 28 days in the heats of hardening whirh have been reported might he the rise is very gradual, although it continues throughout the
Puoverntxr. 1932
1 N D U S T I< I A I, .4 N D E N G I N E E H I N G C 15 E hl 1 S T R Y
&month period and in mme cases produces quite a fair increase. At the later ages the values for the various cements remain in approximately the same order which they have a t 3 days. PAIRED EXPERIMENTS As regards the contributions made by the individual constituents to t.he total heat evolution of a cement, consideration will first be given to those pairs of cements in which but one item was intentionally varied. As there was but a single pair for each, the results must be regarded more as indications than a8 having real quantitative significance. The only variation of this nature whicli was made in clinker was that with respect to magnesia. Cements 2085 and 2092 are the compositions concerned. Their analyses are sum. ciently close so that in respects other than magnesia not marc than a calorie or two of difference in the heats would be ex. pected on the basis of the mathematical analysis which follows. Nevertheless, cement 2092, which contained roughly 2.5 per cent more magnesia, exhibits at all ages the lower heat of hardening, and the differences are 2.7, 5.6, 8.8, 3.1, and 4.9 calories, or 1.1,2.2,3.5, 1.2, and 2.0 calories for each per cent of magnesia. Comparison of cement 2085 with 2086, arid of cement 2090 with 2003 shows no significant difference, indicating that the additional gypsum in samples 2086 and 2093 was without appreciable effect. Likewise, the plaster of Paris in sample 2087 has not caused it to have heats of hardening nigniEcantly different from those of sample 2085. Mmrion OF MATHEMATICAL ANALYSIS h c e e d i n g now to the analysis of the group, there arc fonrteen clinkers represented by the cements of Table I. Ornib ting cements 2086, 2087, and 2093, which were prepared from the same clinkers as others of the series but with variations in the amount or nature of the retarder, there remain fourteen cements, one for each clinker. Of these, sample 2170 was prepared so late that the W d a y data are still lacking. Consequently, it is desirable to disregard it for the time hcing, leaving thirteen cements, corresponding to thirteen Gddy different clinkers, for which the heats of hardening. for 3, 7, 28, 90, and 180 days have been determined. These thirteen cements and the heats of hardening which were found for them have been subjected to matliematieal analysis by the method of least squares to obtain the contribution made by each per cent of each compound to the total heat of hardening, on the assumption that the heat of liardeninp for each cement, at each age can be represented by t,hc linenr relationship: k, (% 4Ca0.AI,0,.Fe20J -4 k, (% 3Ca0.AL10s) f kr (% 2CaU SiO,) k, (% 3Ca0.SiOr) = hent, evolved per gram cement
+
in which the percentages nre those in cement and tlie k's are constant for any given age and method of making and curing the specimens, and for any Portland cement composition, irrespective of the relative proportions of its compounds. In other words, after carrying through an analysis on the thirteen eemcnts a t a given age, there are obtained on this basis four constants which represent, respectively, the heat evolved by 0.01 gram of each of the four compounds. Or they may be expressed as the cont.ribution of each per cent (on neight of cement) of each of the four compounds to the hmt evolved during the hardening of one gram of cement. The stated assumption neglects to take into a.ct:ount the pffect of the gypsum and of the magnesia. \'ariat,ioii in the amount of the former had been indicated hy the tests already dincussed to be without effect. Although it, may still have an effect, but one which is relatively insensitive to change, there is no way of evaluating it from the data a t hand, since t,lre
1211
gypsum is preueiit in all of tlie cements and is in constant amount in those chosen for this analysis. Moreover, since in wmmercial practice it is added to nearly every cement in about this amount, the result of allowing its effect to be absorbed into those reported for the other compounds would scarcely interfere with the practical utility of the values ohtained. As regards magnesia, in a prelinii~iaryanalysis a constant for t h k oxide was carried as an unkiior~mto he determined the
Los ANGELEXC o ~ . i s ~ mUNDER r Covs~nuc~rov same as for the other compounds; but, owing to the fact that the mannesin had been intent,ionally varied in amount in but one cement, and the ai:tual variations (indicated by chemical analysis) in the other cements were slight, the values obtained for the various ages were no greater than thcir probahle errors. Thus, for the group of thirteen the values were: nilUp
a 7
CdOiiS8
Day8
-0.4 1.1 0.0 i 1 . 0
28 90
*
Corlorie* -0.5 * I . I
+0.9
*:.u
There is nu obvious trend with age, arid the average value is zero, which makes it appear that in the mathematical analysis t,he magnesia merely acted as a catchall bo reduce the effectof chance discrepancies. Since in this capac,ity it would tend to alter slightly tho best values of tlie other compounds for general use, it was elirniiiated from the mathematical analysis. The comparison already reported between cements 2085 and 2092 did indicate a negatirn d u e for the effect of magnesia, hut the data are too meager to warrant assigning a numerical value to it on that hasis. Whatever its real amount, the effect of its omission is minimized by its being present in only small percentages in these cements, as it also is in commercial cements. The assumpt.ion of linearity of funrtion is in accord with the generally accepted conception of tlie reaction of cement with water as proceeding without interaction betPreen the CONIpounds (other than tlie action of gypsum with the aluminates). I t is obvious, however, that the distribution o f the water to each per cent of each compoimd could be highly dependent upon the relative proportions o f those compounds in a given cement, with consequent lack of linear relationships. Perhaps it is best to mmgniniL.e this asm@ion as R hypotlresis and let it, lie justified by the results of the analysis. One other matter must be given some attention here-the range in specific surface erhihited by these cements. Independent dttta were obtained oii one normal cement composition ground to several different fiuenesses, and it was found t,liatthe percentage increase in heat evolution was only about half of the percentage increase in fineness even a t 3 days.
1212
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 24, No. 11
TABLE11. CONTRIBUTION OF INDIVIDUAL COMPOUNDS TO HEATOF HARDENING COMPOUND 3CaO.AlzOa 3CaO.SiOz 4CaO~AlzOa~FezOs 2CaO.SiOi
(Contribution, in calories. of each per cent in cement to heat evolution of one gram of cement) 3 DAYS 7 DAYS 28 DAYS 90 DAYS Probable Probable Probable Probable Value error Value error Value error Value error
Value
Probable error
1.70 0.983 0.29 0.195
2.18 1.206 0.73 0.526
fO.ll f0.029 *0.10 f0.024
f0.20 10.064 *0.18 10.046
1.88 1.100 0.43 0.181
fO.19 f0.049 f0.16 f0.041
These data were obtained as a part of another investigation and will not be reported in detail here; but, if it may be assumed that the findings are roughly characteristic of the other compositions as well, the effect of the range in surface exhibited by the cements of the present series is much less than might have been suspected. Furthermore, no correlation between the specific surfaces and the amounts of the compounds is evident; to the extent that the differences in specific surface are random ones, it is to be expected that their effect would show up in the magnitude of the probable errors rather than in the actual values found.
2.02 1.142 0.48 0.436
*0.20 10.054 f0.18 10.045
1.88 1.224 0.47 0.552
180 DAYS
10.18 &0.049 h0.16 *0.041
with the extent of their variation. The variation in the probable errors a t the different ages is also noticeable. This is to be expected because of the limited number of compositions upon which the analyses were made. TABLE111. DIFFERENCES BETWEEN EXPERIMENTAL HEAT VALUESOF CEMENTS AND VALUES CALCULATED FROM MOST PROBABLE VALUES FOR CEMENT COMPOUNDS AGEOF CBXENTPASTE,DAYS:
3
7
12.66
28
90
PROBABLE ERROR, CAL.: *2.54
180
f2.31
*1.36
2122 1390 -2.7 -0.5 -2.9 -3.8 2123 1450 $2.60 +2.2 +1.9 -1.1 2092 1470 $2.1 $1.2 +2.9 -0.3 2088 1480 $5.3 $1.3 $5.5 $7.7 2096 1500 -3.6 -3.1 -1.7 $1.3 2085 1530 +0.8 -2.8 -3.8 -1.3 +0.9 +1.5 $2.2 -0.1 2094 1560 2124 1570 $2.8 $4.0 $2.6 $1.2 2089 1580 -0.5 -5.0 -4.1 -2.2 2090 1600 -3.5 -1.4 -2.2 -3.7 2125 1620 -6.7 -3.5 -3.6 -0.9 2095 1630 +0.7 $1.3 -0.4 +0.7 2091 1670 f1.7 $4.8 $3.7 $2.6 2170 1530 $5.5 +1.0 $4.3 Plus sign indicates that experimental value was the smaller.
$0.4 -1.2 -0.3 +1.3 -0.2 -2.7 +1.5 $2.8 -1.3 0.0 -2.2 -1.0 +2.9
CEMEKT SP. SURFACE,
12.33
Differences
Sq. cm./g.
CONTRIBUTION OF THE INPIVIDUAL COMPOUNDS TO THE HEAT OF HARDENING M05T PROBABLE VALUE
...
5
R 3 728901803 7 28901803 7 28901803 72890180 AGE OF SPECIMEN IN DAYS
The manner of calculation consisted in employing the mathematical method of least squares. By this method the observation equations of the form presented previously were reduced to only four weighted equations. These derived equations, being equal to the number of unknowns to be determined, were then solvable by successive elimination of unknowns. The probable errors of the values thus obtained were calculated by use of the weights which analysis of the derived equations showed them to possess. The probable error as here used is defined as an error of such a magnitude that the probability of making an error greater than it in any given observation is equal to the probability of making one less than it. The method conformed throughout to standard practice in the adjustment of unconditioned indirect observations of equal weight. (The heat evolutions determined for each cement were considered to be of equal weight.) RESULTSOF MATHEMATICAL ANALYSIS The results of these analyses are shown in Table 11. The differences between the heats of hardening calculated for each cement a t each age by means of these values applied to the data of Table I (after converiion of the latter to a cement basis) and the heats of hardening obtained experimentally are given in Table 111,together with the probable error calculated for each age. I n the latter table the results have been applied to cement 2170 also, which, because its data are incomplete, had not been included in the analysis. The specific surfaces of the cements are recorded again in Table I11 for comparison. Figure 2 shows graphically the data of Table 11. The probable errors vary considerably from one compound to another, which is consistent with the different percentages a t which the compounds are present in the different cements and
...
As regards the magnitudes of the probable errors in the total heats of hardening as shown in Table 111, in no case is the value greater than twice the 1.5 calories which might be expected as calorimeter error alone. As there are undoubtedly errors in the analyses sufficient to alter appreciably the actual percentages of the compounds, the agreement obtained is considered to be fully as good as could be expected. FIGURE 3 CORRELATION BETWEEN HEAT OF AND A FUNCTION OF" TRICALCIUM COMPOUNDS
/@'
ARE
++!
30
,
,
40
50
60
70
I
!
80
90
Examination of Table I1 or Figure 2 shows that the compounds, ranked in descending order on the basis of the magnitude of the heat evolution during the first 3 days, are: tricalcium aluminate, tricalcium silicate, tetracalcium aluminoferrite, and P-dicalcium silicate. Thereafter there is an increase in the value for each compound, but the same order is in general maintained. The values for the ferrite and dicalcium silicate keep close together, however, a t the bottom of the scale, with one reversal of order shown by the analysis. The predominance of the values for the tricalcium compounds and the close agreement of those for the other two compounds
1213
Norernb~r.1%3?
iii:ihe a iuiictiou of tlrc tricnlciurii coi~i~ ~ o i i ~alone i d s a fairly good nieasure of t i l e
heat evolution. This is shown in t”g ‘ I urc 3 i n wliieli t,he %day atid 1XO-dny hrrtt~s arc p1ot.ted against (~rorcentngc 3(’a(1 . ~ SiO,) 4-2.1 (Iicrcentaye 3Ca0..llzOlj.’ This sini]de Simrtion is a iisoiiil one Sur qiiirk rough approxitrirrtion of tlie relative r;tnriilirig of two reriiriit,a (differing oii1.v in miiiposition) i n puiiit of lieat cwliit,ion. However, since cement compositioiis are generally reported only hi term;: of the osiilc coniliositiun, tile II( lating the cotnpoiinds further coniplicates tlie matt,er. This renders desirable the interpretation of the lieat data in terrna (if oxide eompositioii. SOCII an alternate t,rcatineiit is also devirable from mrtnin viitwpoints simply Ixxiiiise it docs ari,id the theory of the mineralogical constitution of clinker. Sinw tlie percentage of iiach ~:ompoiiiidis a linear Furictioii of t,lie percentages of the oxides (e),the desired transforniation may readily he made. The results are sliowii in Table IV. Iii ailplying these data to cements, tlie percentage of lime nnist he corrected for lime present in the retnrdcr as calcium sulfate. TABLEIV. HEAT01 H,uri%xrua
1.v TEEMS OF
OXIDE
CoMPOsITtONS
3dnys
noi.
?days Cn!
CaO
13.40
-ta.92
Pel08
--?i.7@ -3.2 -1.1
-0.XU --3.2 -1.5
sio,
AhOr
28dsya (!Ol. +:3 a 1
-4
03 -.Ll -0.1
-4.55
-+:3.29 -4.05 -2.0
-11.4
1-0.4
+8.28 -2.9
Tlie ariiouiit to be subtracted is 0.7 tiiiies tlic ailrootit of SO8 which is reported in tlie analysis. Any utieoinbint.d or free lime should also be subtracted if it can be deterniined. The effect of free lime on the lieat evolution lias not, been deterniiiied experinientally, hut, to tlie extent to which it has hydrated or carborinted prior to the use of the ceinent, it proliably lias no very direct eflect. Its presence, h v e v e r , indicates that there is more dicalciiitri silicate and less tricalcium silicate t,han would otlierwise l x the case, and this situation is taken care of hy subtracting the free lirne friim tlie total lime. The values in Table IV are not ofl’erad as applic,able when, owing to widervariation in the relativeamouritsof oxidcs, com1 at this funetiun, t h e vaiues oi the Iiestr of hardening st the varioii~ages were averaged for ehob compound, the meiln value for tbe ferrite and disaleium ailioste was eirbtrsoted from the YSIUCS ior t h e tiiaaioiurn si& este sad tdcslaium alumionte. and, msiniainijnp the r h o between the latter, they were adjusted t o the basia of 1.0 lor tricalcium silirete. T h e bnsia for this is the following: Let n = % SCeO.SiO* b = % 3Cs0-.43*01 c % 2CeO-SiOn % 4CaO.AinOaFe:Oa If 2CnO-SiOzand 4CnO.AinOxFerQ evolve the s ~ m heat e m i unit. tbsii Kla 1 Klb Klc = h a t evolved = H . Rut c K a - a - b , vilere K4
+
~
+
is the sum KaKd = H .
-
f i x oompounds. Benee. a ( K I - K i
+ b(Ks-Kd +
or thehellieroivedvnrieslinesriy with thefunctiunu(Kr-Kr) if K. may be considered t,o be constant.
+ bW-K,,),
p i r i i i i d s arc formed o t h e r t h a n tliofie actually present in the compositioiis liere studied. There arc several practical aspects froin wliicli the reliability {if tlie matliemnt.ieal analysis presented in this paper inay Lie viewed --the rnngnit.ude of the probable errors, tlie tirue seqiienne of t,lie i ~ &ants obtained for t w i h cmipou~iil,a i d the ~ a l i i e s of t.liose vonst,imtstiieniselvei. The reitwnaliloness of tlic probalile errors footid for tlie iiircct, (leterininat,ions 11a s alrendy recciyd cormtietit,. Tlie p h a l d c errors ealciilated for the compounds are in all eases Icsr, tliari the valiies of the c:oirst,ni~tswhich were olit;tined; in the Case of the tricalcium wni~,oimdswhich evoke tlic must lieat, tlir values are . S W C ? F ~ t,irrtes its Inrgc :is t,he calciilnted wrors. .A.ltliougli in some case8 the trends of t,lie values with irrc%t.ased age of specimen show R u h n t i o n , they all pruceed lipwards, and iii general the irregiilnrities are no greater than miglrt lie expected from ihe niagiiitiides of tlie proiialile errors. There exists, fortunately, a sat,isfact(rry means for estiiiiat.iiigtlie reliability of the high m l i i e s obtained for trica.lciurn aluminate. Tliorvaldson, Ilromn, and Pcaker have deterniined the lieat of bydration of the piire eompound (8). All things considered, tlie valires calculated for the later ages in tlio present study are in excelleiit agreenrent with their value of 214 calories per gram a t 20’ C. for conversion to the stable hexahydrate. Eveii their value of 261 i:alories per gram for conversion to the most higlily Iiydrated form (11.6 II,O) for wliieh they obtained data is not excessively greater. As regards tricalcium silicate, wliidi is believed to IiydrolyAe with attendant hydration of the liberated lime, the known heat evirlut.ion of this latter reaction is capable of accounting for a large proportion of that indicated for the silicate by the matliematicel analysis. The heat of hydration of the lime which rvoilld Imve to he removed from the tricalciurn silicate to convert it. to dicalciutn silicate amounts to 0.68 calorie per 0.01 grain of the original silicate, arid thus corresponds rouglily to the difkrcnee in tlie values obtained for these two i:ompounds. AtT,,,CAT,OK
OF
R
ills
‘ro Commnci.u, CEMEFTSANI)
(~oMhfEFlC1.4L 1’RACTlCE l i r applying tlie results of this analysis t u coiiiinercial cement.s, it is not to he expected that the agreement hetwoen calculated and esperinient.al \ d u e s will he as good as that shown in Table 111. The commercial cements will vary in amouut of free lime, which, due to partial carbonation, cannot be determined accurately. Tliey will also differ in amount of minor eoiistituents, whose influence, though believed to be small, is not definitely knon,n. The specific surfaces of msny of tlmri will he outside the range in thin experimental group, and their histories will lie different. They will have been fired at different temperatures, cooled at different mtes, stored for different periods nnder different conditions. Ihfferent srnall percentage8 of water w-ill have heen drawn from t.he atmosphere t,o produce surface hydration. Tlrese eircumstances exert an influence on otlier properties of cement,
-
1 N 11 u s1' I< I ti I ,
151i
'
4 l\i
u
1:' N G 1 u 15 E' 11 1 N G
c 11 1:.
\I 1 s
r I
