I
A. 9. COMSTOCK, S. J. JURNACK,' and R. W. MOONEY Chemical and Metallurgical Division, Sylvania Electric Products, Inc., Towanda, Pa.
Precipitation of Calcium Hydrogen Orthophosphate Four- Variable Statistical Design
This investigation of precipitation variables, using a standard statistical technique, provides a method for predicting the physical properties of calcium hydrogen orthophosphate powder obtained a5 the product of the reaction between calcium chloride and diammonium hydrogen phosphate
PHYSIC-~L
properties of powders entering solid state reactions determine, to a large extent, the physical properties of fired products and affect the reactivitbof the mix. From this standpoint. the most important raw material used in the preparation of calcium halophosphate phosphors is calcium hydrogen orthophosphate. Therefore, a study \vas made of the effects of temperature of precipitation, concentration of reactants. and rate of addition of diammonium hydrogen phosphate to calcium chloride on the physical properties of calcium hydrogen orthophosphate made by the reaction : (NHa)zHPOa
+
+
CaC1z = CaHPOa 2NHaC1 (1)
There is evidence to indicate that the first precipitate formed when solutions of calcium and HPO?-- ions are mixed is calcium hydrogen orthophosphate (70). Exploratory work confirmed these results. However, prolonged washing of the precipitate, especially a precipitate formed a t temperatures of 60' C. and below, caused a transition to the calcium hydrogen orthophosphate dihydrate or calcium hydroxyl apatite structure. For this reason, the temperature region studied was limited to precipitation temperatures above GO0 C. to avoid phase transitions.
po\vder to a specific variable of precipitation unless all other variables are held constant. Ho\vever> to examine one variable at a time Lvhile holding all others constant bvould require a prohibitively large number of esperiments and \vould give no information on the interactions. .4 central composite design for regression analysis as developed by Box and others (2) \vas applied. A s in a standard regression analysis the response J , a dependent variable. is described as a function of the independent variables under investigation such that
y = f (21,
X?,
x3, X d
calcium chloride and diammoniurn hydrogen phosphate concentration, 0.5 to 2.0 moles per liter; and rate of addition, 10 to 350 nil. per minute. T h e ranges of the indeprndent variables define the boundaries of the experimental region. For ease of calculation and identification. the variables \\.ere coded by Equations 4 through rvhich give rise to Table I .
= bo f bixi f
4- b 3 ~ 3+ 64x4
XI
(3)
=
(iYHa)?HP04 concn. - 1.25
I
Present address, Rutgers University,
0.375
(6)
addition rate - 180 U5
(7)
A composite design involving four independent variables requires 30 esperiments consisting of a 24 factorial. a n octahedron in four dimensions, and six center points ( 5 ) . T h e center points were replicated to give an estimate of the experimental error. T h e design was
Coded vs. Uncoded Values of Independent Variables Ranges of these variables define the experimental boundaries
Uncoded Values ~~
It is difficult to ascribe a change in some physically measured property of the calcium hydrogen orthophosphate
(5)
x, = __
z? (CaC12
Statistical Design
(4)
0.375
where fi is the predicted value of the dependent variable under investigation, and the regression coefficients are the least square estimates of the parameters of the response surface. For this investigation, the independent variables \vere studied over the folloLving ranges: temperature, 65' to 95" C.;
Table I.
80
CaCly concn. - 1.25
(2
b 2 ~ 2
-
7.5
= --
T h e model equation fitted for each response \vas
8
temp. ___-.
x, =
C'oded Talues 2
1 0 -1 -2
XI (temp.), 95.0 87.5
80.0 72.5
65.0
C.
11
~~
~
~~~
[(SHr)rFlPO, roricii. 1,
concn.),
moles/liter
inoles,'liter
I;
(addn. r a t e ) , nil. !min.
2.0
2.0
350
1.63 1.25 0.88 0.50
1.63 1.25 0.88
265
0.50
180 95 10
VOL. 51, NO. 3
MARCH 1959
New Brunswick, X. J.
325
run in three blocks. T h e complete blocked design in the random order in which it was run is given in Table 11. Two of the blocks are the half replicates of the factorial with two center points in each block. The other block is the octahedron with the remaining two center points. By running this design in blocks, a first order response could be estimated after running the first block. If the primary purpose were to find the optimum conditions, the method of steepest ascent (2) might be used to reach an optimum region in which to run additional experiments. I n this investigation, the design limits were set to study a desired region and conditions outside of these limits were not considered. T h e data were analyzed at the completion of each block. A complete analysis of variance (Table 111) was made on all three blocks taken as the composite design. I n the interpretation, although statistical analysis indicated higher order response, the experimenters felt that the first order models derived gave sufficiently practical descriptions of the response in the region of investigation. The derived equation in each case is referred to as the prediction equation. Using this, the response at any point within the experimental region can be predicted. The precision of the prediction equation gradually decreases upon moving out from the center of the design to the extremes. Experimental
T h e precipitation of calcium hydrogen orthophosphate was carried out by adding diammonium hydrogen phosphate solution to calcium chloride solution contained in a 6-liter round-bottom flask submerged in a constant temperature Xvater bath (rk0.01' C.) The diammonium hydrogen phosphate solution was gravity fed using a 4-liter aspirator bottle as a reservoir. The air entering the reservoir was metered by Brooks Rotameter Flowmizers: giving a fairly accurate and reproducible method of measuring the rate of addition. The diammonium hydrogen phosphate solution was passed through a helical glass heat-exchanger just prior to addition, thereby raising the temperature to that of the calcium chloride solution. During precipitation, the contents of the reaction flask were agitated vigorously, and the p H of the reaction was followed with a Beckman Model H-2 glass electrode pH meter. T h e precipitations were stopped at p H values which varied linearly from 5.26 a t 65' C. to 4.97 a t 95O.C. The final pH values were varied as it was shown that the entire pH curve shifted to lower values with increasing
326
temperature. These values were arrived at by studying the p H changes with temperature over the region 25' to 95' C. The p H of the calcium chloride solution was normally slightly basic, but with the first few milliliters of diammonium hJ-drogen phosphate, the pH dropped sharply to 3 to 4 because of hydrolysis of the ammonium ions. With continued addition, the p H gradually increased until nearing the equivalence point where it rose fairly sharply to a value of between 6 and 7 because of the more easily hydrolyzed HPOI-ions. The point of maximum slope was calculated and used as the point to which the reaction should proceed giving the values listed above. This point of maximum slope was always somewhat past the equivalence point, thus ensuring complete precipitation of calcium hydrogen orthophosphate because of excess HPOI-- ions. The resulting precipitate was filtered, washed free of chloride with deionized water, and dried at 110' to 120' C. The following measurements were made on the dried powders. X-RAYIDENTIFICATION. X-ray powder patterns were taken using nickelfiltered CuKw radiation M ith exposure times of 3 to 4 hours a t 35 kv. and 15 ma.
Run NO.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Identification was made by comparison with diffraction patterns listed recentlkby McIntosh and Jablonski ( 8 ) . ANALYTICAL DETERMISATIONS. Percentage calcium was determined by precipitation of calcium sulfate from ethyl alcohol followed by ignition at 750' C. Percentage phosphorus was determined by measuring the percentage transmittance of a solution obtained by adding ammonium molybdate and acetone to an aliquot of the sample after treatment with perchloric acid. The results \rere compared to those obtained from standard samples by the use of a Beckman Model B spectrophotometer. The material was assayed by firing to the calcium pyrophosphate structure. Percentage yield was also determined on all samples. DENSITYMEASUREMENTS. The absolute densities of the samples were determined using conventional pycnometer techniques. The bulk densities were measured in a Scott paint volumeter. The container. a 1-inch cube, was neither vibrated nor tapped to induce packing. PARTICLE S I Z E h I E A S U R E M E S T S . Three different methods of measuring particle size were used. The first was the standard Fisher sub-sieve size (SSS) measurement commonly used for control
Table It. Box-Wilson Design and Experimental Data Partirle Size Measurements Coded Values of Independent Variables B.E.T. surSedimen- Bulk face area, Fisher tatiori density, x4 Xa dopl grams/ 51 22 f(NHd2- (addn. sq. meter4 SSS, microns micro~is cu. in. gram (temp.) [CaCl?] -HPOal rate)
Yield,
70
Block I 1 2
3 4 5 6
7 8 9 10
-1 0 -1 +l +l -1 +1 0 +1 -1
-1 0 +1 -1 -1
-1 +1 0 -1 +l
-1 0 +1 -1 -1 +l +1
-1 0 -1 +1 -1
+1
+1 +1 0 -1
-1
$1
-1 +1
+1
0 +1 +l
0 +1 -1
0
11.0 9.4 3.5 21.1 8.9 13.6 9.2
11.1 12.3 13.0
4.2 4.5
2.2 3.0 3.2 2.2 5.0 1.3 2.9 3.4 5.6 2.1
3.6 4.5 4.4 3.5 4.0 4.9 3.9
3.8 2.6 2.7 1.3 4.5 2.2 3.3 2.5 1.2 4.0
3.9 4.4 5.1 3.4 5.0 3.9 4.1 3.6 3.2 3.5
2.8 1.4 3.1 3.3 1.6 11.5 1.3 2.9 4.2 1.6
3.2 3.5 3.8 4.0 3.2 5.8 2.7 3.2 3.4 3.1
4.7
4.7 5.6 5.3 6.7 9.0 2.8 5.3 5.3 8.8 3.7
97.0 95.9 98.5 90.5 94.4 95.2 94.6 93.4 94.0 92.8
6.4 5.6 5.5 2.4 6.4
93.0 94.2 95.6 98.3 96.3 95.1 91.8 92.0 94.8 91.6
Block I1
1 2 3 4 5 6 7 8 9 10
+1 -1 0 -1 +1 0
+1 -1
0 +l +l
-1
0
-1
0 +1
4-1 -1
-1 -1
-1 +1 -1
$1
-1
-1
1 2 3 4
0 -2 0
0 0 -2
5
0 0 0 0 +2 0
0 0 0 0 0 0 -2 +2
0 -1 +l +1 -1
10.9 13.1 10.5 10.8 5.4 11.1 11.2 18.0 15.2 18.4
5.9 6.4 6.2 2.9 8.5
Block 111
6 7 8 9 10
0
0
10.6 11.6 20.9
0
0
10.1
0 0 0 0
+2 -2 0 0 0 0
13.0 3.8 27.9 7.6 9.4 15.4
0
0
0
12
0 0
5.6 2.9 7.8 5.7 3.6 12.3 5.9 5.0
7.5 3.9
93.3 95.7 90.0 94.5 94.9 94.5 90.0 96.4 95.2 95.3
PRECIPITATION VARlABLES purposes. Because of variations between instruments it is difficult to reproduce a set of readings from one instrument to another. However, the readings should bear the same relationship to each other. The second method used was the determination of particle size distribution from optical measurements of sedimentation rates. The principles of this method have been thoroughly treated in several texts (4,7 ) , and its specific application to phosphor systems has been discussed by Bergin and Butler (7). This method yields values of don. the median optical diameter, and u, the standard deviation or spread of the distribution. The third method employed was the determination of surface area by the \\-ell-known gas adsorption method based upon the B.E.T. theory ( 3 ) . However, for routine evaluation of many samples, the modified procedure and apparatus developed by Starkweather and Palumbo ( 7 7) was used. X tabulation of the experimental data is given in Table 11. Results Exploratory work had shown that, a t precipitation temperatures of 60' C. and below, the washed precipitates were usually mixtures of calcium hydrogen orthophosphate and calcium hydrogen orthophosphate dihydrate-the relative amount of each dependent upon the temperature of precipitation and the amount of washing. .4t temperatures of 50' C. and below with high rates of addition. calcium hydroxyl apatite was often formed. However, a t 65' C. and
above. only anhydrous calcium hydrogen orthophosphate \vas present. T o check these results, x-ray diffraction patterns were taken of the extremes in the design, and in all cases the product was identified as anhydrous calcium hydrogen orthophosphate. I n view of these results, it is not surprising that the percentage of calcium and phosphorus, absolute density, and assay are essentially constant over the range of conditions studied (Table IV). The percentage of calcium is slightly high whereas the percentage of phosphorus is slightly low, thus indicating the possibility of the presence of small amounts of calcium hydroxyl apatite. However, in general, the analytical data confirm the presence of calcium hydrogen orthophosphate. The prediction equation for per cent yield is:
+
tj = 94.29 - 0 . 7 1 ~ 1
+
0.96~2 1 . 1 5 ~ 34- ( - 0 . 2 4 ~ 4 ) (8)
Equation 8 shows that increasing the temperature decreases the yield and increasing the concentration of either reactant increases the yield. The prediction equation for bulk density is: tj = 5.79
+ 1 . 3 6 ~ 1+ ( - 0 . 1 2 ~ 2 ) + (-0.55~3) - 1.48~4 (9)
The rate of addition and temperature of precipitation obviously have a predominant effect on the bulk density, as evidenced by the relatively high coefficients derived for b , and 6 4 , with the trends being in line with the experimenters' u priori expectations. The
Table 111.
A Complete Analysis of Variance Was Made on All Three Blocks Mean Squares Fisher Degrees of Bulk density B.E.T. sss lield Source Freedom 2 0.44 7.68 0.78 1.28 Blocks Linear hi
1 1 1 1 4 6 10 3
bz b3 b4
Quadratic Interactions Lack of fit Error
Table IV.
44.47 0.40 7.32 53.19 2.43 0.82 0.92 0.04
2.98
340.51 50.46 89 70 43.30 5.77 5.48 0.60
Theoret.
a
12.32 22.42 32.20 1.40 2.70 3.60 2.89 1.32
Analytical Data Are Constant over the Ranges Studied Assay Abs. (CaHPOd), Density, Ca, 5% p, % % Grams/Cc. 29.4
22.8
30.0 0.51
21.6 0.32
Expt.
Av. Std. dev. Literature value
14.88 2.47 0.35 45.10 7.45 0.39 1.33 0.11
(9).
... 98.8
0.71
effect of concentrations was not evidenced until block 111 was run, showing that only high or low concentrations within the selected ranges have any significant effect on bulk density. The analysis of the Fisher SSS data indicate a response similar to that previously found for bulk density-Le., increasing the temperature increases the Fisher SSS, whereas increasing the rate of addition decreases the Fisher SSS. The latter may be somewhat exaggerated by the result of run No. 6, block 111. The prediction equation for Fisher SSS is :
0 = 3.09
+ 0 . 7 8 ~ 1+ 0 . 3 2 ~ 2f (-0.12~3)
-
1.37~4 (10)
I t was immediately apparent from the earliest experiments that the calcium hydrogen orthophosphate system did not easily lend itself to the sedimentation method of determining particle size. The data usually deviated from a lognormal distribution a t low diameters, thus making the selection of do, and u somewhat arbitrary. T o correct this situation, several different dispersing agents and methods of dispersing were tried with negative results. The do, values are tabulated in Table 11, but as the values for u did not vary appreciably, they are not included. The validity of the sedimentation data obtained from the calcium hydrogen orthophosphate measurements was questioned, and no interpretation or use of these data were attempted. One possible expfanation for the inadequacy of this method is that the reactions of calcium hydrogen orthophosphate in solution are very complicated and likely to lead to colloidal suspensions. Thus, various degrees of aggregation may exist in solution leading to results which depend upon the degree of dispersion. This could cause the experimental difficulties in fitting the data to a log-normal distribution. The prediction equation for B.E.T. surface area is: ij = 12.27
+ (0.35~1)- 3 . 7 6 ~ 21 . 4 5 ~ 3+ 1 . 9 4 ~ 4 (11)
Equation 11 leads to increasing values of surface area with increasing rates of addition in agrerment with earlier observations. However, the most pronounced effects are those due to concentration, where decreasing the concentration of either reactant also leads to increasing surface area values. This again may be exaggerated by the results of runs 3 and 7 in block 111.
2 * 920 2.85 0.03
Discussion The effects of temperature of precipitation, concentration of reactants, and VOL. 51, NO. 3
0
MARCH 1959
327
rate of addition on the physical properties may be compared by using the derived prediction equations for yield, bulk density, Fisher SSS, and B.E.T. surface area (Equations 8 through 11, respectively). T h e values enclosed in parentheses in these equations d o not produce large changes in their respective responses, and for all practical purposes their effect may be disregarded. The same trends are evidenced in the Fisher SSS and the bulk density data. Thus, increasing the temperature causes both to increase and increasing the rate of addition causes both to decrease. Thus, Fisher SSS and bulk density are measuring the same fundamental property of the powder. Another way of expressing bulk density is as the void fraction:
f
I
x3=+ I
-2
0
-I
+I
+2
X I (TEMPERATURE)
I
x3
= 0
x,
=-I
-+2 -
z
0 k
=
1 - (&/do)
(12)
\\.here f = void fraction db = bulk density d, = absolute density
B+l-
a
LL
0
0-
w l-
a (I
The bulk density units of grams per cubic inch must be converted to grams per cubic centimeter to agree with the absolute density units before insertion into Equation 12. This calculation gives some insight into the actual volume occupied by solid particles as opposed to the volume that the powder in its usual form occupies. The void fractions calculated for the precipitations varied between 0.74 and 0.96, illustrating that the most dense powder contained 747, voids and the least dense powder 96% voids. Obviously, calcium hydrogen orthophosphate is a very loosely packed solid. T h e Fisher SSS and bulk density data are very different from the B.E.T. results. T h e analysis of variance (Table 111) shows that the B.E.T. surface area is markedly affected by the concentrations of the reactants with the lowest concentrations giving the highest surface area. T h e rate of addition term is consistent throughout, as higher rates of addition should increase the surface area or decrease the particle size in agreement with the Fisher SSS predictions. Increasing the temperature decreases the solubility of calcium hydrogen orthophosphate (6) ; therefore, a decreasing yield \vith increasing temperaturc is most difficult to explain. Similarly, no explanation is offered for the effect due to concentration. In general, the changes due to yield are small (90.0 to 98.5%), whereas major variations in certain physical properties are brought about by the same conditions. Hence, theconditions of precipitation Ivould probably be selected on the basis of the desired physical characteristics letting the )-ield fall where it may. T o illustrate graphically the reproducibility of the data and to a limited extent the geometry of the Box-Wilson design,
328
Y
-2
h
-
+2.
z 9 k
g+l.
Acknowledgment
a LL
0
w
-5
Q -
*-I.
X
-2 -
/
/
the bulk density data have been plotted us. x1 (temperature of precipitation), x3 (diammonium h>-drogen phosphate), and xq (rate of addition) in the figure. The effect of calcium chloride concentration has not been considered, as Equation 3 has shoivn that its contribution is insignificant. T o plot bulk density against three independent variables. three plots of bulk density values obtained a t varying x1 and x 1 values have been made a t x3 = -1, x 3 = 0, and x 3 = +1. This includes all the data, except the tWo points for X Q = -2 and x3 = f 2 , and assumes that .Y? makes no significant
INDUSTRIAL AND ENGINEERING CHEMlSTRY
-
-
x“-l
contribution to thr r c s u l ~ s . This assurn],tion is corroborated by tlic excellent repmducibi1it)- of the data lvhen I,.. t 3 , and .Y, equal zero. ’l‘hc diagonal 1inr.s tepresent intersections of these planes by Equation 3 for the given values or hulk density. The same trends are evident from this graphical representation as have already been found from the prediction equation for bulk density. Similar plots may be constructed fur thc other dependent variables. The difference in the results for thc at: IOUS properties leads to several interesting possibilities. Thus. by precipitating a t high temperatures and low roncentrations, the resulting powder should have a high Fisher SSS and bulk density coupled \virh a high B.E.T. surface area. Exactly the opposite conditions-i.e., low temperature and hi@ concentrations should yield a pobvder uf low Fisher SSS and bulk density lvith a low B.E.T. area. -4 high B.E.T. area can only be had at the expense of the yield. The yield might be improved somewhat by precipitating a t the lowest temperature that gives calcium hydrogen orthophosphate, but this would also lead to a low Fisher SSS and low bulk density. In a similar manner, because yield is not affected by rate of addition, it is possible to decrease the Fisher SSS particle size or increase the B.E.T. surface area by increasing the rate of addition lcithout affecting the +d.
The authors are indebted to G. J. Meisenhelter for the analytical determinations, to T . J. Veleker for the x-ray identifications, and to R. C. Selson’s metallurgical laboratory for the measurements of B.E.T. surface area and sedimentation particle size. In addition. the advice of R. L. Goldsmith on the statistics is gratefully acknowledged. literature Cited (1) Bergin, M. J., Butler K. H.: J. Hectrochfm. SGG. 101, 149 (1954). ( 2 ) Box, G. E. P., Wilson, E=. P., J . Roy. Statist. Sac. B13, 1 (1951). (3) Brunauer, S., Emmett, P. H., Teller, E., J . A m . Chem. SGC. 60, 309 (1938). (4) Dalla Valle, J. M., “Micromeritics,” Pitman Publishing Co., S e w York. 1951. (51 Davies, 0. L., “Design and Analysis of Industrial Experiments,” Hafner Publishing Co., S e w York, 1954. (6) Elmore, K. L., Farr, T. D., IND. ENG. C H E h i . 32, 580 (1940). (7) H y d a n , G., “Small Particle Statistics, Elsevier, Kew York, 1953. (8) McIntosh, A. O., Jablonski, W. I,., Anal. Chem. 28, 1424 (1956). (9) MacLennan, G., Beevers, C. A., Acta Cryst. 8 , 579 (1955). (10) Neuman, W. F., Neuman, M. W., Chem. Reos. 53, 1 (1953). (11) Starkweather, F. M., Palumbo, D. T., J . Electrochem. SOC.104, 287 (1957). RECEIVED for review February 10, 1958 ACCEPTED September 10, 1958
