Hardness of Salts Used in Industrial Crystallization - ACS Symposium

Chapter 4

Hardness of Salts Used in Industrial Crystallization

Downloaded by UNIV OF TENNESSEE KNOXVILLE on August 16, 2015 | http://pubs.acs.org Publication Date: September 21, 1990 | doi: 10.1021/bk-1990-0438.ch004

J. Ulrich and M. Kruse Verfahrenstechnik, FB 4, Universität Bremen, Postfach 330 440, D-2800 Bremen 33, Federal Republic of Germany

The ultra-micro-hardness of inorganic and organic salts has been measured for 15 substances. These are products usually produced in industrial crystal lization. The hardness-force-dependency was examined and data are compared to those from literature. In the case of potassium nitrate a strong direction depend ency of the hardness was observed. Also effects of im purities in the crystal lattice were analysed. In the end an attempt has been introduced to calculate the hardness of crystals from a physical model.

The design of the c r y s t a l l i z e r s f o r the c r y s t a l l i z a t i o n of aqueous solutions i s depending on the usual informations f o r plant design and on the k i n e t i c data of the material t o c r y s t a l l i z e . The material fixes the physical properties, the c r y s t a l growth and the n u c l e a t i o n behaviour. S p e c i a l d i f f i c u l t i e s e x i s t i n f i n d i n g the n u c l e a t i o n data. Here a s p e c i a l focus i s on the secondary nucleat i o n , because t h i s i s i n most cases the dominating n u c l e a t i o n mechanism. From t h i s secondary nucleation process, i t i s again the part which i s originated by mechanically introduced energies which i s of most i n t e r e s t . In other words the questions are: How many abrasion p a r t i c l e s (secondary n u c l e i ) are produced i n a c r y s t a l l i z e r ? Which rules and laws can be used t o c a l c u l a t e the number of the nuclei? F i n a l l y how i s i t possible t o do a scale up operation, and how i s the e f f e c t of a d i f f e r e n t products t o be considered? There i s a parameter necessary t o describe the abrasion r e s i s tance of each c r y s t a l l i n e substance. This abrasion resistance must be c o r r e l a t e d with parameters of the power input devices such as pump or s t i r r e r diameter or the s t i r r e r t i p speed. The abrasion r e s i s t a n c e of the c r y s t a l l i n e p a r t i c l e s produced by secondary n u c l e a t i o n i n i n d u s t r i a l c r y s t a l l i z a t i o n processes i s t h e r e f o r e a p h y s i c a l property of the substance. So f a r there i s no p h y s i c a l property known containing a l l information about t h i s abrasion r e s i s 0097^156/90/0438-0043$06.00/0 © 1990 American Chemical Society

In Crystallization as a Separations Process; Myerson, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

44

CRYSTALLIZATION AS A SEPARATIONS PROCESS

tance and the influence of the fracture mechanics on the c r y s t a l s . According t o (1-8) the Vickers hardness could be a f i r s t step i n defining such a material property. Up t o today i t has been impossible t o measure reproducible microhardness data of non-metallic c r y s t a l s . This was due to the too high indentation forces of commercial a v a i l a b l e hardness t e s t i n g devices. Today with the new ultra-microhardness devices, which allow to reduce the indentation force down to 5 - 10* N, i t i s no longer the l i m i t i n g problem to measure the Vickers hardness of such b r i t t l e crystals. Results of the Vickers hardness of 15 inorganic and organic s a l t s w i l l be presented. The hardness-force dependency, and the e f f e c t s of d i r e c t i o n dependency were examined. The measured values of the Vickers hardnesses were taken for an attempt to prove a model to c a l c u l a t e the hardness. This model describes the hardness purely by physical properties of the substances. The use of such a model may be an approach f o r the d e s c r i p t i o n of the abrasion r e s i s t a n c e of s a l t s . Data describing the abrasion resistance could help i n the understanding and interpretation of secondary nucleation phenomena.


4

Experimental Set-Up and Measurements The ultra-micro-hardness of the s a l t s are measured according t o Vickers. The Vickers hardness i s calculated from the length of the diagonals of a p l a s t i c indentation i n the surface of the material to be t e s t e d by a diamond pyramid. I f there e x i s t s no d i r e c t i o n dependency the hardness indentation has a quadratic shape. The Vickers hardness for a single indentation i s calculated from the average value of the two diagonals. Equation 1 shows how t o c a l c u l a t e the Vickers hardness H from the indentation force F and the average of the two diagonal lengths d of the indentation. The constant 1854 i s v a l i d f o r the case that the force F has the unit pond and the length d the unit millimeters. v

H

v

= 1854 • F/ d

2

(1)

A l l experiments were carried out with an ultra-microhardness measuring device (Vickers-hardness) produced by Anton-Paar-Company. I t i s attached to a microscope with an adapted photo camera. The force of indentation, the time of indentation and the time-gradient of the indentation force can be selected and adjusted separatly. For most substances used i n the experiments an i n d e n t a t i o n f o r c e greater than 0.1 N leads t o cracks or even l i f t - o f f s at the edges or the ends of the diagonals of the indentation produced by the Vickers pyramid. Therefore the values of the measured hardnesses have a large spread and u s u a l l y are not reproducible. Most of the l i t e r a t u r e data were produced at a time where ultra-micro-hardness devices were not available, so that forces larger 5-10" N have been used. 2


4.

ULRICH&KRUSE

Hardness ofSalts Used in Industrial Crystallization

Results A comparison o f the r e s u l t s of our experiments with data from l i t e r a t u r e are shown i n Table 1. Our experimental data were found with an indentation force of 2 - 10" N, a time of indentation of 10 s, and a gradient of 10* N/s. The shown data represent an average of at least 10 single measurements for a l l the d i f f e r e n t substances. In most cases of the l i t e r a t u r e data no information about t h e experimental conditions are available. Therefore an exact comparison i s unfortunately not possible. 2


2

Table 1: Comparison of the Vickers Hardness Measurements and the Data from L i t e r a t u r e

Vickers Hardness H

Substance

Own Results

RbJ KJ KC1

6.3 9.7 10.6

KBr NaCl

11.0 22.3

KNO3

CsBr C i t r i c acid MgS0 • 7 H 0 NH A1(S0 ) 12 H 0 KA1(S0 ) 12 H 0 K S0

47.1 51.6 52.6 66.8 74.9 75.7 112.6

CuS0 - 5 H 0 LiF NaClOj

118.7 122.7 134.6

4

2

a

4

4

2

2

a

4

2

2

2

4

4

2

V

Literature

5.7 6.1 9.9 9.7 10.0 7.2 17 24 18 13 17

(£) (£) (2) (1Q) (11)

(£) (£) (11) (12) (9) (£)

56 56 102 130

(9) (2) (£) (13)

102 118

(£) (£)

The force-dependency of the Vickers hardness was measured f o r s e v e r a l s a l t s . This e f f e c t i s shown i n Figure 1 e.g. f o r sodium c h l o r a t e . With an increase of the indentation f o r c e the V i c k e r s hardness decreases, e.g. up t o 40 % for sodium chlorate. The photos of indentations by the Vickers pyramid i n a sodium chlorate c r y s t a l are presented i n Figure 2 and give an idea of r e s u l t i n g cracks and l i f t - o f f s . This cracks are due t o too high indentation forces (the indentation force t o be seen i n the Figures are: 2a, 2 • 10* N; 2b, 4 • 10' N; 2c, 0.25 N; 2d, 0.6 N). In the case of potassium n i t r a t e the Vickers hardness indentat i o n s have not a quadratic shape. This i s due t o a d i r e c t i o n dependent hardness i n the c r y s t a l l a t t i c e of t h i s material. The d i r e c t i o n dependency can be explained with an anisotropic e f f e c t i n the l a t 2

2


45



46



4. ULRICH&KRUSE

Hardness of Salts Used in Industrial Crystallization

t i c e . The force-dependency o f the Vickers hardness isshown i n the p l o t i n Figure 3. In the diagram there are two curves of the Vickers hardness r e s u l t i n g always from the same indentation image. The hardness values d i f f e r by a f a c t o r of two. The one curve r e s u l t s from the data o f the longer and the other from the shorter diagonal o f each intendation. This d i r e c t i o n dependency was so f a r only observed for the case of potassium n i t r a t e . Also the e f f e c t of impurities i n a c r y s t a l on the Vickers hardness was analysed. In Figure 4 are shown the force dependency curves of the Vickers hardnesses of a pure sodium chloride c r y s t a l and a sodium chloride c r y s t a l grown i n a solution with an impurity of 10 % urea. The hardness of the pure sodium chloride c r y s t a l i s up t o 25 % higher than the hardness of the impure c r y s t a l . Modelling of the Hardness The mathematical modelling of hardness from physical properties was not the object of research work f o r quite a time, since there had been no p o s s i b i l i t y t o v e r i f y the t h e o r e t i c a l r e s u l t s with the experimental data. F i r s t attempts (14-16) described only the hardness o f simple cubic c r y s t a l s of the type AB as a function o f t h e i r interatomic distances and the valencies of the atoms. This i s shown i n Equation 2: H «

B

• [*i • «2l / r

m

(2)

Here i s H the hardness, s and m are empirical constants, Z are the valencies of the atoms, and r i s the interatomic distance. Another p o s s i b i l i t y t o c a l c u l a t e the hardness from p h y s i c a l properties (17) i s given i n Equation 3: {

H

= A

• U

• r"

3

(3)

Where the hardness H i s combined with the l a t t i c e energy o f the ABtype c r y s t a l U, the interatomic distance r and an empirical constant A. Equation 3 was modified by the authors (18.19) so that i t r e s u l t s i n Equation 4: H

= K

• T

D

• r'

3

(4)

Here the hardness H i s connected with a constant K, the Debye temperature T and the interatomic distance r . A l l these models f o r the c a l c u l a t i o n of the hardness need emp i r i c a l parameters which cannot be explained by physical properties of the c r y s t a l s . This problem i s solved i f the hardness of c r y s t a l s i s described as a volumetric cohensive energy as suggested by Plendl e t . a l . ( 2 0 ) . Then the hardness can be w r i t t e n as the r a t i o o f the cohensive energy U to the molecular volume V, as to be seen i n Equat i o n 5. D

H

= U

/ V

American Chemical Society

Library 115516th St., N.W. In Crystallization as a Separations Process; Myerson, A., et al.; ACS SymposiumWnhlngton, Series; American Chemical Society: Washington, DC, 1990. D.C. 200$

(5)

47


48


Figure 2a. Photo of an indentation i n a sodium chlorate c r y s t a l with an indentation force of 2 * 10" N 2

Figure 2b. Photo of an indentation i n a sodium chlorate c r y s t a l with an indentation force of 4 - 10' N 2



4.

ULRICH&KRUSE


Figure 2c. Photo of an indentation i n a sodium chlorate c r y s t a l with an indentation force of 0.25 N

Figure 2d. Photo of an indentation i n a sodium chlorate c r y s t a l with an indentation force of 0.6 N


49


0

+

+

+

+

2

4

of the indentation

Hardness data resulting from the short diagonal

+ ++

Hardness data resulting from the long diagonal of the indentation

8 10 Force (10e-2 N]

Figure 3. Force-dependency of the Vickers hardness for potassium nitrate.

Time of indentation: 10 3; gradient: 10e-2 N

10

20 -

30

40

Vickers hardness 50



Figure 4. Force-dependency of the Vickers hardness f o r pure sodium c h l o r i d e and sodium c h l o r i d e c r y s t a l s grown i n a s o l u t i o n with an impurity of 10 % urea

Vickers hardness 301


u%

52


An analyses of the measured microhardness of non-metallic leads to new atomic subdivisions namely t o :

substances

- the 'hard-core' substances, e.g. L i F , CaO, SiC^, and - the 'soft-core' substances, e.g. NaCl, CaF , S i , Ge. 2


In Table 2 the r e s u l t s are shown f o r the c a l c u l a t e d volumetric cohensive energies of c r y s t a l s with NaCl-type s t r u c t u r e and t h e i r measured Vickers hardness. Table 2: Comparison of the Measured Vickers Hardness and the Calculated Volumetric Cohensive Energy f o r NaCl-Type Crystals

Substance

Volumetric Cohensive Energy (201 [kcal / cm J

Vickers Hardness

3

KJ KC1 KBr NaCl LiF

2.9 4.4 3.8 6.7 21.0

9.7 10.6 11.0 22.3 122.7

This l a s t model The hardness H properties. C l a r g e s t common unit charge and

of the hardness i s modified and given i n Equation 6. i s according to (21) a function of several p h y s i c a l i s the constant defined i n Equation 7, Z i s the valency of the atoms, f i s the f o r c e constant per r represents the interatomic distance.

s t r #

0

H

=

C

str

. •

Z

C tr. - N • p • r s

• 3 0

f / r

0

/ 2 •M

r

(6) (7)

Here N i s the Avogadro number, p i s the density of the c r y s t a l and M the the reduced mass of the atoms. In Figure 5 a comparison i s presented f o r the calculated Vickers hardness (Equation 6) and the measured V i c k e r s hardnesses f o r several i o n i c bonded c r y s t a l s with NaCl-structure. The comparison of the measured and c a l c u l a t e d V i c k e r s hardnesses i s of acceptable quality. With t h i s p h y s i c a l model of the hardness i t should a l s o be p o s s i b l e t o compute the V i c k e r s hardnesses of s a l t s with a more complicated l a t t i c e structure than the NaCl-structure. This may be an approach f o r a d e s c r i p t i o n of the abrasion r e s i s t a n c e of s a l t s . Such a d e s c r i p t i o n of the abrasion resistance could be useful i n c a l c u l a t i n g the secondary nucleation rates• r


4.


ULRICH & KRUSE

Measured Vickers hardness


100

-

-

10

/*KC\

KBr-

-

KJ" RbJ"

/ /

-

i

i

i

i i i i ii 10

1

I i i 100

Calculated Vickers hardness Figure 5. Comparison of the c a l c u l a t e d and measured V i c k e r s hardness f o r NaCl-type c r y s t a l s

Acknowledgment s The support of t h i s project by the Deutsche Forschungsgemeinschaft (DF6) i s g r a t e f u l l y acknowledged. Legend of Symbols A d F f H H K M

v

r

constant length of diagonals indentation force force constant per unit charge hardness Vickers hardness constant reduced mass


53


54 m N r, r 8 T U V D


p

0

constant Avogadro's number interatomic distance structure factor Debye temperature l a t t i c e energy or cohensive energy molecular volume valency density

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Tai, C. Y.; McCabe, W. L . ; Rousseau, R. W. AIChE Journal 1975, 21, 351. Offermann, H.; Ulrich, J . Verfahrenstechnik 1980, 14, 815. Ulrich, J . Ph.D. Thesis, RWTH Aachen, Aachen FRG, 1981. Offermann, H.; Ulrich, J . In Industrial Crystallization 81; Jancic, S. J.; de Jong, E. J., Ed.; Elsevier: Amsterdam, 1981, p 313. Heffels, S. K. Ph.D. Thesis, TH Delft, Delft NL, 1986. Pohlisch, R. J . Ph.D. Thesis, TU München, München FRG, 1987. Offermann, H. In Industrial Crystallization 87, Nývlt, J.; Zacek, S., Ed.; Elsevier: Amsterdam, 1989, p 121. Mersmann, A.; Sangl, R.; Kind, M.; Pohlisch, J . Chem. Eng. Tech. 1988, 11, 80. Engelhardt, W. v.; Haussühl, S. Fortschr. Miner. 1965, 42, 5. Balaramaiah, A.; Pratap, K. J.; Hami, Babu, V. Cryst. Res. Technol. 1987, 22, 1205. Plendl, J . N.; Gielisse, P. J.; Mansur, L. C.; Mitra, S. S.; Smakula, A.; Tarte, P. C. Applied Optics 1971, 10, 1129. Chin, G. Y. Trans. Amerc. Crystall. Asso. 1975, 11, 1. Ridgway In Crystallization; Mullin, J . W.; Butterworths: London, 1972 Goldschmidt, V. M. In Geochemische Verteilungsgesetze: Oslo, 1927 Reis, A.; Zimmermann, L. Z. physik. Chem. 1922, 102, 298. Friedrich, E. Fortschr. Chem. Phys. phys. Chem. 1926, 18, 1. Wolff, G. A.; Toman, L . ; Field, N. J.; Clark, J . C. In Halbleiter und Phosphore; Schön, M.; Walker, H., Eds., Braunschweig, 1958, p 463. Ulrich, J.; Kruse, M. Cryst. Res. Technol. 1989, 24, 181. Ulrich, J.; Kruse, M. Chem.-Ing.-Tech. 1989, 61, 962 Plendl, J . N.; Gielisse P. J . Phys. Rev. 1962, 125, 828. Plendl, J . N.; Gielisse P. J . Z. Kristall. 1963, 118, 404

RECEIVED April 12, 1990


Hardness of Salts Used in Industrial Crystallization - ACS Symposium

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