The influence of Na2O on the hydration of C3A II. Suspension
hydration
Citation for published version (APA):
Spierings, G. A. C. M., & Stein, H. N. (1976). The influence of Na2O on the hydration of C3A II. Suspension hydration. Cement and Concrete Research, 6(4), 487-496. https://doi.org/10.1016/0008-8846(76)90077-6
DOI:
10.1016/0008-8846(76)90077-6
Document status and date: Published: 01/01/1976
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CEMENT and CONCRETE RESEARCH. Vol. 6, pp. 487-496, 1976. Pergamon Press, Inc
Printed in the United States.
THE INFLUENCE OF N a 2 0 ON THE H Y D R A T I O N OF C3A. II. S U S P E N S I O N HYDRATION.
G.A.C.M. Spierings and H.N. Stein L a b o r a t o r y of General C h e m i s t r y
T e c h n o l o g i c a l University, Eindhoven, The N e t h e r l a n d s
(Communicated by H. F. W. Taylor)
(Received March 25, 1976)
A B S T R A C T
The influence of N a g O on the h y d r a t i o n of C ~ A was studied in s u s p e n s i o n s from the start of th~ r e a c t i o n onwards. The heat e v o l u t i o n rate in very early stages of the hydration, m e a s u r e d at v a r y i n g N a O H
c o n c e n t r a t i o n s , and SEM,indicate that at
NaOH c o n c e n t r a t i o n s larger then 0 . 1 M the r e a c t i o n
m e c h a n i s m differs from that in water. In these
solutions the h y d r a t i o n is t h o u g h t to be c o n t r o l l e d at first by a more or less amorphous Ca(OH) 2 layer.
Der E i n f l u s s von N a 2 0 auf die H y d r a t i o n des C 3 A w u r d e
u n t e r s u c h t v o m A n f a n g der R e a k t i o n an. Die W ~ r m e -
e n t w i c k l u n g s g e s c h w i n d i g k e i t in den e r s t e n H y d r a t a t i o n s -
stadien, g e m e s s e n bei v e r s c h l e d e n e n N a O H - K o n z e n t r a t l o n e n , und S E M - A u f n a h m e n d e u t e n auf einen anderen R e a k t i o n s - m e c h a n i s m u s bei N a O H - K o n z e n t r a t i o n e n g r ~ s s e r als 0 . 1 M .
In d i e s e n L ~ s u n g e n ist die H y d r a t a t i o n im A n f a n g
b e h e r s c h t durch eine m e h r oder w e n i g e r amorfe Ca(OH) 2- Schicht.
I n t r o d u c t i o n
In a previous paper (I) the influence of N a 2 0 on the
h y d r a t i o n of C3A in pastes was reported. To e l u c i d a t e some of
the aspects of t h e h y d r a t i o n mechanism, e s p e c i a l l y d u r i n g the first m i n u t e s of hydration, C~A h y d r a t i o n in s u s p e n s i o n (w/s = 100) was studied from the start of the h y d r a t i o n onwards using i s o p e r i b o l i c calorimetry.
E x p e r i m e n t a l
Methods for SEM, X - r a y analyses and the a r r e s t i n g of
h y d r a t i o n were as d e s c r i b e d p r e v i o u s l y (I). C o n d u c t i v i t y
m e a s u r e m e n t s were p e r f o r m e d as d e s c r i b e d by de Jong, Stein and Stevels (2).
The heat e v o l u t i o n rates in the s u s p e n s i o n s were m e a s u r e d
using a p r e c i s i o n c a l o r i m e t e r LKB 8700-I. The principles of
these m e a s u r e m e n t s have been d e s c r i b e d by W a d s ~ (3). An
i s o p e r i b o l i c c a l o r i m e t e r consists in p r i n c i p l e of a nearly adiabatic r e a c t i o n vessel in an e n v i r o n m e n t of constant
temperature. The total heat Q(t I) d e v e l o p e d after a certain
h y d r a t i o n time t I can be c a l c u l a t e d from the f o l l o w i n g e q u a t i o n
(4) :
t
Q(t I) = sAT(t I) + 8 ~ T ( t ) d t , w h e r e o--
= heat capacity of r e a c t i o n vessel + contents,
AT(t) = t e m p e r a t u r e d i f f e r e n c e b e t w e e n e n v i r o n m e n t and
tlr r e a c t i o n vessel after time t (presumably),
8 ]AT(t)dt = total heat leak d u r i n g t I seconds. o--
AT(t) was calculated by m e a s u r i n g the change in resistance
of a t h e r m i s t o r AR with a W h e a t s t o n e bridge. The heat leak from
the reaction vessel to the e n v i r o n m e n t was found to be p r o p o r t i o n a l to AT(t).
The e x p e r i m e n t s were conducted with an e n v i r o n m e n t
t e m p e r a t u r e of 25 ° + 0.01oc and the m a x i m u m t e m p e r a t u r e rise in
any e x p e r i m e n t was ~.7°C.
The m a t e r i a l s used and methods for d e t e r m i n i n g sodium and c a l c i u m were those d e s c r i b e d p r e v i o u s l y ( I ) . A l u m i n i u m was d e t e r m i n e d as d e s c r i b e d by Pribil and V e s e l y (5).
H y d r a t i q n of C3A in NaOH Solutions in S u s p e n s i o n s Results
Fig. I shows the cumulative heat e v o l u t i o n for C~A h y d r a t e d
in s u s p e n s i o n in w a t e r and NaOH solutions (w/s = I00)$ Fig. 2
shows the heat e v o l u t i o n rate obtained by d i f f e r e n t i a t i n g the
curves in Fig. I. In all cases the heat e v o l u t i o n rate is high
d u r i n g the first seconds and decreases rapidly as h y d r a t i o n
proceeds. At higher pH (>0.1M NaOH) a second peak in the heat
e v o l u t i o n rate appears w h i c h is a c c e l e r a t e d by increasing NaOH concentrations.
Vol. 6, No. 4 489 C3A, HYDRATION, NaOH SOLUTION
60O C.) "6
/ /
• ooL! /
> --A-- H20 I~/o/ --•-- 0.4 M NaOH f i / - - c ~ - - 2 M NaOH!/
- - ~ ' - - 4 M NaOH I I I I I, I I I I 10 30 60 g0 Time (rain) FIG. 1C u m u l a t i v e heat e v o l u t i o n from C3A h y d r a t e d in water and NaOH solutions
.~ 10 i' '
'-~ st-
2" ® io:
-~o.s
LUK~a
0.1 I 1 ~ " ! I I I I I I 0 o l i • ! ! | ! 0.5 h 0 . 0 5 k " ' a ' l , , , , m.~ ~I | 6 0 80 100 A ~ A - - H2 0 \ - - m - - 0.1 M NaOH :'~,~'. --'-- 0.4M NaOHA
. \ " . ' , ,
- - o - -2 M
.,oH
~j. 0 . 1 - ,.,\\m.=.v_.
~,~ ~ m ~ A ~ / " v ~ " " I I ~ 1 ' I I I I i I I I 1 3 5 10 20 40 60 Time (rain) FIG. 2Heat e v o l u t i o n rates of C3A h y d r a t e d in water and N a O H solutions
I X tz A
.9,=0
w ~ tll - j . m I ! ! I I I I I I 2 3 4 N;IOH Concentration (M) FIG. 3 I n i t i a l h e a t e v o l u t i o n r a t e v e r s u s the N a O H c o n c e n t r a t i o n the N a O H c o n c e n t r a t i o n . This " i n i t i a l " h e a t e v o l u t i o n rate is the m a x i m u m r a t e of i n c r e a s e of the t h e r m i s t o r t e m p e r a t u r e , w h i c h is r e a c h e d a few secondS a f t e r the f i r s t c o n t a c t b e t w e e n the r e a c t a n t s . A t i m e lag a r i s e s b e c a u s e of the d e l a y in the r e s p o n s e of the t h e r m i s t o r . A t low N a O H c o n c e n t r a t i o n (<0.1M) the i n i t i a l h e a t e v o l u t i o n r a t e d e c r e a s e s r a p i d l y w i t h i n c r e a s i n g N a O H c o n c e n t r a t i o n w h i l e h i g h e r N a O H c o n c e n t r a t i o n s e f f e c t o n l y a m i n o r a d d i t i o n a l d e c r e a s e . X - r a y a n a l y s e s of the h y d r a t i o n p r o d u c t s are s h o w n in T a b l e I. Fig. 4 s h o w s SEM's of the h y d r a t i o n p r o d u c t s on the s u r f a c e s of p a r t i c l e s a f t e r 10 s e c o n d s and 10 m i n u t e s h y d r a t i o n . In w a t e r w i t h o u t N a O H a d d i t i o n the p l a t e - l i k e h y d r a t e s are, in m a n y cases, o r i e n t a t e d m o r e or less p e r p e n d i c u l a r l y to the s u r f a c e of a p a r t i c l e i n s t e a d of the p r e d o m i n a n t l y p a r a l l e l o r i e n t a t i o n in p a s t e h y d r a t i o n (1). .TABLE I X - r a y D a t a for h y d r a t i o n of C 3 A in N a O H s o l u t i o n s N a O H H y d r a t i o n t i m e C 2 A H 8 C 4 A H 1 3 C 3 A H 6 C 3 A (M) (min) 0 1 0 w - w v s 0.04 10 - V W v w vs 2 10 - w V v w vs 2 1200 - - S s Fig. 5 s h o w s the c h a n g e in c o n d u c t i v i t y of C 3 A s u s p e n s i o n s d u r i n g the h y d r a t i o n in H20 and d i l u t e N a O H s o l u t i o n s D i s c u s s i o n The d e c r e a s e in c o n d u c t i v i t y (Fig. 5) a f t e r a c e r t a i n h y d r a t i o n t i m e (5.7 h for a s u s p e n s i o n of C 3 A in water) i n d i c a t e s the p o i n t d u r i n g the h y d r a t i o n at w h i c h the c o n v e r s i o n ofh e x a g o n a l h y d r a t e s i n t o C 3 A H ~ b e c o m e s i m p o r t a n t e n o u g h to c a u s e the s o l u t i o n to l e a v e the m e £ a s t a b l e p o i n t of c o e x i s t e n c e of
C2AH8, C 4 A H I ~ and a q u e o u s s o l u t i o n (9). B o t h the c o n d u c t i v i t y
e x p e r i m e n t s ~nd the b e h a v i o u r of the s e c o n d h e a t e v o l u t i o n p e a k shows t h a t this c o n v e r s i o n is a c c e l e r a t e d w h e n the N a O H
Vol. 6, No, 4 491 C3A , HYDRATION, NaOH SOLUTION
a b c d e f FIG. 4 S E M ' s of C 3 A h y d r a t e d in s u s p e n s i o n (w/s = 100) for a 10 sec in H 0 d 10 m i n in H 0 10 sec in 0 ~ I M N a O H ~ 10 m i n in 0 ~ I M N a O H 10 s e c in 2 M N a O H ~ 10 m i n in 2M N a O H
i I
J
2 u'~ o • r E o • - - 2i/
' ~ ' . ~ . _ _ . J ,.,= ta a f.nIf
~ v ~ v . 1 == 1 i / t n l2 4
6 Time (rain) I i i IO.Ol
M
NaOH
j
\
O.02M
NaOH
\
.
.
.
.
- \ .
\
\ i i I I I rk 0.0&N Na0H v / v - v - v - v - v
v--v--v--v-
7 ~ V _ _ V _ _ V/ v ~ v
' ~ - - v - - , ~ p ~ . . , . . , . , v - - v _ _ v _ _ v _ _ v _ _ i ~ "\
1
/ " i
]
5
÷
v~-- ~0.1M hlaOH Time
(h)
FIG. 5InCrease in specific c o n d u c t i v i t y w i t h regard to initial c o n d u c t i v i t y of suspensions of C3A in w a t e r and aqueous NaOH
c o n c e n t r a t i o n increases. In 0.1M NaOH, the c o n d u c t i v i t y
increases at the time of the second heat e v o l u t i o n peak (compare
Figs. 2 and 5). For suspensions w i t h o u t NaOH, a very early
appearance of the second peak and the a c c o m p a n y i n g c o n d u c t i v i t y d e c r e a s e that were o b s e r v e d in pastes (I) were not found,
p r e s u m a b l y because of d i f f i c u l t y in n u c l e a t i o n of C3AH &. Thus,
the influence of NaOH on the second peak in s u s p e n s i o n ~ is always an a c c e l e r a t i n g one.
In the early h y d r a t i o n stages, the heat e v o l u t i o n rate in pastes is about equal to that in suspensions after the same time. This is remarkable in view of the d i f f e r e n t o r i e n t a t i o n of the p l a t e y crystals in the hydrate layer in the two cases, and rules out a direct screening action of the hydrates.
The SEM results show that a hydrate layer exists on the
C3A surface. Because of m i s f i t between the latter and the
hydrates, some space will exist between them. Three p o s s i b l e
e x p l a n a t i o n s of r e t a r d a t i o n of C3A h y d r a t i o n will be considered. I) This space is filled by an aqueous solution saturated towards the anhydrous C~A, the h y d r a t i o n rate of the C3A then being d e t e r m i n e d e i t h e r - b y the d i f f u s i o n of ions out of the space c o n c e r n e d and of water into it, or by the growth of the h e x a g o n a l hydrates in the layer.
2) Feldman and R a m a c h a n d r a n (10) p r o p o s e d that the h y d r a t i o n of C3A is i m p e d e d , n o t by hydrates, but by the b l o c k i n g of
m o v e m e n t s of surface d i s l o c a t i o n s by a d s o r p t i o n of ions, such as
Vol. 6, No. 4
493
C3A, HYDRATION, NaOH SOLUTION
r e c r y s t a l l i z a t i o n of h e x a g o n a l h y d r a t e s because the latter is a c c o m p a n i e d by some changes in the c o n c e n t r a t i o n s of these ions.
3) An aqueous s o l u t i o n occurs in the space between the C~A and the h e x a g o n a l hydrates, in w h i c h conditions differ from th~se
in the o u t s i d e solution; this leads to the formation in this
space of an amorphous solid that can m a t c h the C.A surface on an
atomic scale more closely than can a h e x a g o n a l h~drate (11). The
role of the h e x a g o n a l hydrates is then an isolating one, and the rate d e t e r m i n i n g step is the t r a n s p o r t b e t w e e n the crystals of the h e x a g o n a l h y d r a t e s of ions, w h i c h tend to attack the
r e t a r d i n g agent.
R e g a r d i n g these three r e a c t i o n m e c h a n i s m s the following remarks can be made:
A c c o r d i n g to the "saturated solution" m e c h a n i s m the heat e v o l u t i o n rate at t ÷ 0 c o r r e s p o n d s to a s i t u a t i o n in w h i c h the d i s s o l u t i o n of C3A is not h i n d e r e d by hydrates, and follows the e q u a t i o n
C3A + 6H20 ~ 3Ca2+(aq) + 2AI(OH) 4 (aq) + 4OH-(aq) However, the d e p e n d e n c e of the heat e v o l u t i o n rate at t ÷ 0 on the N a O H c o n c e n t r a t i o n is too weak, e s p e c i a l l y at higher c o n c e n t r a t i o n s , to be c o m p a t i b l e w i t h the mechanism, at least if equal volumes of liquid are assumed to be saturated per unit of
time in all cases. This m e c h a n i s m could a c c o u n t for the facts
only if w i t h i n c r e a s i n g NaOH c o n c e n t r a t i o n e i t h e r a larger v o l u m e w o u l d be a c c e s s i b l e to s a t u r a t i o n by C3A , or increasing
c o n t r i b u t i o n s of hydrate p r e c i p i t a t i o n to the heat e v o l v e d at
t ~ 0 are assumed. Both a l t e r n a t i v e s are improbable; the former
b e c a u s e large NaOH c o n c e n t r a t i o n s promote p r e c i p i t a t i o n of
Ca(OH) 2, the latter because this p r e c i p i t a t i o n is an e n d o t h e r m i c process.
A c c o r d i n g to the m e c h a n i s m p o s t u l a t e d by F e l d m a n and
R a m a c h a n d r a n (10), the influence of increasing NaOH c o n c e n t r a t i o n s at t ~ 0 is caused by i n c r e a s i n g d i f f i c u l t y in m o v e m e n t of
dislocations; the levelling off w i t h higher NaOH c o n c e n t r a t i o n s
is due to all surface sites being o c c u p i e d by OH- ions, the d e c r e a s e of the heat e v o l u t i o n rate is due to gradual e x h a u s t i o n of surface dislocations, and the second peak can be a s c r i b e d to
a d e c r e a s e in OH concentration, as has indeed been o b s e r v e d in
s u s p e n s i o n s at that p a r t i c u l a r stage of r e a c t i o n by
de Jong, Stein and Stevels (9). However, this effect is small
(the pH changes from 12.2 to 12.1), e s p e c i a l l y when c o m p a r e d
w i t h the OH c o n c e n t r a t i o n s present, for instance, in 4M N a O H
w h e r e the second peak remains quite r e m a r k a b l e (Fig. 2). Thus,
the data do no~ support a surface d i s l o c a t i o n m o v e m e n t inhibition
by a b s o r b e d OH ions.
The following m e c h a n i s m appears to be c o m p a t i b l e w i t h the results: In NaOH solutions of high c o n c e n t r a t i o n the amount of Ca 2+ g o i n g into solution as a result of h y d r a t i o n of the C3A
m u s t be small. A l u m i n a t e ions may go into solution but Ca 2+
ions stay behind, their charge being c o m p e n s a t e d by OH- ions. R e a r r a n g e m e n t into c r y s t a l l i n e Ca(OH) 2 is p r e v e n t e d by the
a d j a c e n t C3A. The r e s u l t i n g p r i m a r y layer thus formed p r e v e n t s
surface closely because of its in situ formation. Figs. 4a-c show that after 10 seconds h y d r a t i o n in water a structure c o n s i s t i n g o f ~ a t e s r e m i n i s c e n t of the hexagonal hydrates is formed, while in 2 M NaOH a dense layer is formed w h i c h m i g h t be capable of p r e v e n t i n g contact between the C3A and the solution. Some H2Oand OH- will p e n e t r a t e through this layer and react with
aluminate ions from the C3A_to form AI(OH)~-. These aluminate
ions replace part of the OH ions in the l~yer, and at some
distance f r o m the C3A r e a r r a n g e m e n t into h e x a g o n a l hydrates may occur, as is shown by X-ray analyses (Table I) and SEM
(Fig. 4d-f).
The d e c r e a s e in the heat e v o l u t i o n rate with time (Fig. 2) is a s c r i b e d to the layer b e c o m i n g thicker, and the second peak to r e c r y s t a l l i z a t i o n of the hydrates into C3AH6, w h i c h affects the c o n c e n t r a t i o n gradients in the v i c i n i t y of the C3A
s u f f i c i e n t l y to d e s t a b i l i z e the p r i m a r y layer. This h y p o t h e s i s
would explain the absence of X-ray r e f l e c t i o n s due to c r y s t a l l i n e Ca(OH) 9 and the presence of only weak lines due to the hexagonal hydrates (Table I).
It appears from the c o n d u c t i v i t y curve thatpafter the
formation of the layer seen in Fig. 4b, some hydrate nucleates
in the s u r r o u n d i n g liquid. This is shown by the c o n d u c t i v i t y
m a x i m u m found after about I m i n u t e (Fig. 5 ; the SEM shown in Fig. 4b was taken after 10 sec., w h i c h is before the
c o n d u c t i v i t y maximum). This supports the e x i s t e n c e of two
hydrates: one at the C~A surface, a second one somewhat further
away from it. The second one is the one seen in Figs. 4e-f° and
is thought to be a d i s o r d e r e d form of one of the hexagonal hydrates p l a y i n g an isolating rather than a r e t a r d i n g role.
The m e c h a n i s m d e s c r i b e d is not n e c e s s a r i l y the m e c h a n i s m
o p e r a t i v e in H~O or in Ca(OH) 2 solutions. On the contrary, the
shape of the he~t e v o l u t i o n rate at t + 0 versus the NaOH
c o n c e n t r a t i o n graph (Fig. 3) suggests that a d i f f e r e n t m e c h a n i s m becomes o p e r a t i v e when the NaOH c o n c e n t r a t i o n exceeds 0.1M.
H y d r a t i o n of 0 . 2 5 N a 2 0 . 2 . 7 5 C a O . A I 2 ~ 3 in S u s p e n s i o n s Results
The total heat d e v e l o p e d up to a certain h y d r a t i o n time and the heat e v o l u t i o n rate at the time c o n c e r n e d are both shown in
Fig. 6. The~Dtal heat liberated after a certain h y d r a t i o n time
and the h e a t ~ b e r a t i o n rate during the N0.25C2.75 A h y d r a t i o n are somewhat lower than for C3A (Figs. I and 2].
In Fig. 7 the c o n d u c t i v i t y of a suspension of N 0 ~ 5 c 2 . 7 5 A is
plotted against time. At certain times d e s i g n a t e d b~-
A, B, C and D the hydration was arrested and X-ray analyses of the solid phases and chemical analyses of the liquid phase were
performed. Table II shows the results of these analyses.
D i s c u s s i o n
When N0.25C 2 ~ A is hydrated in suspensions with w/s = 100
no second peak in" heat evolution rate curve appears (Fig. 7).
The total heat d e v e l o p e d up to a certain h y d r a t i o n time is only slightly less than the total heat developed during the hydration
V o l . 6, No. 4 495
C3A, HYDRATION, NaOH SOLUTION
FIG. 6 C u m u l a t i v e h e a t e v o l u t i o n and h e a t e v o l u t i o n r a t e d u r i n g the h y d r a - t i o n in s u s p e n s i o n (w/s = 100) of N 0 . 2 5 C 2 . 7 5 A in H 2 0 ii
~
_io
I ° ~ ° I °
c • • o , >o o~ 0.1l-, O ~ _To /
0.011 I I ' ' ' ' ' ' I 10 3O 60 90 T i m e (rain) FIG. 7 S p e c i f i c c o n d u c t i - v i t y of a s u s p e n - s i o n (w/s = 100) of N 0 . 2 5 C 2 . 7 5 A in H 2 0 " O , - O u 2 ._~ i i I I I i I I Ik"A
2
I I I I 1 2 3 4Time
T A B L E IIA
! ITime
I t I5
6
?
(h)
T i m e ( m i n ) C 2 A H 8 A 3 v w B 32 w C 200 s D 4 1 0 s X - r a y and c h e m i c a l a n a l y s e s d a t a for h y d r a t i o n of N 0 . 2 5 C 2 . 7 5 A in H 2 0 c o n c e n t r a t i o n in m m o l / l C a 2 + C 4 A H 1 9 C 3 A H 6 N 0 . 2 5 C 2 . 7 5 A A I ( O H ) 4 Na + - - vs 1.54 1.47 0.58 - v w s 0.62 0.75 1.22 m m w 0.06 0 . 9 1 1 . 8 6 - vs v w 0.42 1 . 9 6 2.40 of C3A. T h u s the h y d r a t i o n c h a r a c t e r i s t i c s of N 0 . 2 5 C 2 75 A in s u s p e n s i o n s are a l m o s t s i m i l a r to t h o s e of C 3 A , w h i l e in p a s t e s t h e r e e x i s t s a s i g n i f i c a n t d i f f e r e n c e (1). T h e s i m i l a r i t y b e t w e e n the h y d r a t i o n in s u s p e n s i o n of C 3 A a n d N 0 . 2 5 C 2 . 7 5 A is tobe expected in view of the small NaOH c o n c e n t r a t i o n s effected by the former (Fig. 2). Again it appears (see ref. I) that the NaOH c o n c e n t r a t i o n in the solution is more important than changes in solid state properties.
References
I. G.A.C.M. Spierings and H.N. Stein, to be published. 2. J. de Jong, H.N. Stein and J.M. Stevels, J. Appl. Chem.
(London), 18, 9 (1968).
3. J. Wads~, Science Tools, 13, 33 (1966). (Chem. Abstr. 69, 30771 u) .
4. S.R. Domen and P.J. Lamperti, J. Res. Nat. Bur. Stand., 78A , 595 (1974).
5. R. Pribil and V. Vesely, Chem. Listy, 63, 1217 (1969). (Chem. Abstr. 72, 6243v).
6. H.N. Stein, Special Report 90, Highway R e s e a r c h Board, W a s h i n g t o n D.C., p.368 (1966).
7. Gmelin, Handbuch der A n o r g a n i s c h e n Chemie, C a l c i u m Tell B, p.1248, Chemie Verlag, Berlin (1956).
8. F.E. Jones, J. Phys. Chem., 48, 379 (1944).
9. J.G.M. de Jong, H.N. Stein and J.M. Stevels, J. Appl. Chem. (London), 19, 25 (1969).
10. R.F. F e l d m a n and V.S. Ramachandran, Mag. Concr. Res., 18, 185 (1966).
11. W.A. Corstanje, H.N. Stein and J.M. Stevels, Cem. Concr. Res., 3, 791 (1973).
