Q

The specimen thickness should be at least one and a half times the diagonal length; greatest accuracy is obtained with high loads, but loads as small as 0.01 N can be used. However, at lower loads the elastic recovery is of greater importance. For loads lower than 0.5 N the technique is usually described as microhardness testing. The 136° angle between opposite faces of the Vickers indenter (Fig. 10) is based on geometrical similarity to the Brinell indenter allowing for conversions between hardness scales provided the diameter of the impression is 0.375 times the ball diameter (i.e. the angle included between the tangents of a circle under these conditions for the ball indenter is 136°) and the Brinell hardness < 4000 MPa (Cottrell, 1964).

Indenter

Vickers

Brinell

Knoop

Rockwell

Material of which indenter is made

Diamond

Hardened steel or tungsten carbide

Diamond

Diamond

Shape of indenter

Square based pyramid

Sphere

Rhomb based pyramid

Cone

Dimensions of indenter

12J

A = 172° 30'

e = 136

fig. 10 Geometries for various hardness testers. For definitions of terms, see text.

fig. 10 Geometries for various hardness testers. For definitions of terms, see text.

Although hardness measurements on compacts were first recorded by Spengler and Kaelin (1945) using a Brinell indenter and by Nutter Smith (1949) using a Vickers indenter, the specimens used were formulations containing added excipients and hence are of little use for the evaluation of material properties.

An improved analysis of the Vickers hardness of compacts was performed by Ridgway etal. (1969b) using a Leitz microhardness tester with loads of between 5 and 2000 g. Accurate diagonal lengths were determined after lightly dusting the indent with graphite powder. Of the materials studied potassium chloride, hexamine and urea showed little change in hardness with increasing compaction pressure while for aspirin and sodium chloride the hardness increased possibly owing to work hardening. The maximum hardness values reported were 29MPa, 17MPa, 16MPa, 12MPa and 8MPa for sodium chloride, potassium chloride, aspirin, hexamine and urea, respectively. These values are an order of magnitude lower than those generally accepted and hence must be viewed with suspicion.

In many studies on compacts, spherical indenters have been used either fitted to commercially available instruments or custom-built equipment. An example of the former is the pneumatic microindentation apparatus described by Ridgway etal. (1970). This instrument (Plate 4) can apply loads of between 4 and 8g using a spherical indenter 1.5 mm in diameter and measure depths of penetration of 1-6 /*m. Using this apparatus on aspirin compacts, the authors were able to show that hardness measurements at the centre of compacts were higher than those at the periphery, a property for flat-faced compacts confirmed by Aulton and Tebby (1975). However, for compacts prepared using concave punches hardness distribution tends to vary with the degree of curvature (Aulton and Tebby, 1975).

In a modification to the original microindentation apparatus (Ridgway etal., 1970), Aulton etal. (1974) added a displacement transducer to measure the vertical displacement. Co npacts were formed under a compression pressure of 50 MPa and therefore would be expected to have high porosities. They suggested that the elastic quotient index, which is the fraction of the indentation that rebounds elastically, was a measure of the ability of materials to form tablets.

In a further study involving a larger range of materials, Aulton (1981) found that hardness measurements were generally higher on the upper face of the compact than on the lower. However, the differences were material dependent and the hardness measurements reported were 62 MPa, 54 MPa, 51 MPa, 36 MPa, 19 MPa and 13 MPa for sucrose, Sta-Rx, Emcompress, Avicel PH101, lactose (3 anhydrous and paracetamol, respectively. As well as being extremely low, the relative order of the materials is considered to be wrong in relation to the particle hardness (see later).

Probably the most relevant of all the work carried out on hardness measurement on compacts is that of Hiestand etal. (1971) using a spherical indenter attached to a pendulum and that of Leuenberger (1982) and his co-workers (Jetzer etal., 1983a,b, 1985; Leuenberger and Rohera, 1985; Galli and Leuenberger, 1986) using a spherical indenter attached to a universal testing instrument.

In the dynamic pendulum method of Hiestand etal. (1971) a 24.5 mm diameter spherical ball falls under the influence of gravity and the rebound height and indent dimensions are measured (Fig. 11). The hardness is calculated from the expression:

where m is the mass of the indenter, g is the gravitational constant, r is the radius of the sphere, a is the chordal radius of the indent, /j, is the initial height of the indenter and hr is the rebound height of the indenter.

Rg. 11 Schematic diagram of the dynamic pendulum apparatus used by Hiestand et a/. (1971). For definitions of terms, see text.

Rg. 11 Schematic diagram of the dynamic pendulum apparatus used by Hiestand et a/. (1971). For definitions of terms, see text.

In the case of the indenter attached to the universal testing instrument (Leuenberger, 1982) loads of 3.92 and 9.81 N were applied to a sphere of 1.76 mm diameter at a velocity of 0.05 cm min-1; indent diameters were determined from scanning photomicrographs.

In both cases indentation hardness was found to be dependent on the compaction pressure and hence relative density (porosity) of the compact in an exponential manner. While Hiestand et al. (1971) considered extrapolation to unit relative density to be questionable, Leuenberger (1982) used the relationship between Brinell hardness, Hb, of a compact and its relative density, D, to develop a measure of compactibility and compressibility, i.e.:

where Hbmtx is the theoretical maximum hardness as the compressive stress, <jc, approaches infinity and the relative density of the compact approaches unity and X is the rate at which Hb increases with increasing compressive stress. In the equation Leuenberger (1982) has suggested that Hbma describes the compactibility and X compressibility.

Data on indentation hardness using both methods are shown in Table 4. As with the modulus of elasticity, values for hardness vary over two orders of magnitude from the very hard materials (e.g. Emcompress) to very soft waxes. Drugs have intermediate hardness values.

It should be noted that the values recorded are also variable owing to:

1. The intrinsic variability in the specimens. Jetzer etal. (1983a) demonstrated that for aspirin, Avicel PH101, caffeine, a-lactose monohydrate and Emcompress the 95% confidence limits gave 82-101 MPa, 148-189 MPa, 163-416 MPa, 409-659 MPa and 210-1294 MPa, respectively. The increased variability also mirrors the increase in hardness (Table 4) for this series of materials.

2. Work hardening as the compaction pressure is increased. Leuenberger and Rohera (1986) and Aulton and Marok (1981) have clearly demonstrated an increase in the Meyers work-hardening index for a variety of materials.

3. The increase in hardness with increasing indentation load (Leuenberger and Rohera, 1986).

4. The rate of measurement. In a comparison of the dynamic pendulum method of Hiestand et al. (1971) - equivalent to a strain rate equal to that of a high-speed compaction simulator - and the pseudostatic method of Leuenberger (1982), Jetzer etal. (1985) demonstrated that, in general, both methods gave the same hardness for aspirin, caffeine and mannitol. However, the dynamic method was less reproducible.

Table 4 Indentation hardness measured on compacts

Material

Indentation hardness (MPa)

Reference

Sugars a-Lactose monohydrate 515

a-Lactose monohydrate 534

Lactose ß anhydrous 251

Sucrose 1046-1723

Sucrose (250-355#) 493

Drugs

Paracetamol DC 265

Caffeine (anhydrous) 290

Caffeine (granulate) 288

Oxprenolol succinate 262

Hexamine 232

Phenacetin 213

Sitosterin 198

Metamizol 91

Aspirin powder 91

Aspirin FC 87

Aspirin 60

Aspirin 55

Ibuprofen (A) 35

Ibuprofen (B) 162

Alkali halides

NaCl 653

NaCl 313

NaCl (rock salt) 358

KCl 99

KBr 69

Others

Emcompress 752

Avicel PHI02 168

Starch 1500 78

Sodium stearate 37

PEG 4000 36

Castor oil (hydrogenated) 32

Magnesium stearate 22

Sodium lauryl sulfate 10

Leuenberger (1982) Jetzer etal. (1983a) Leuenberger (1982) Leuenberger (1982) Jetzer etal. (1983a)

Jetzer etal. (1983a) Jetzer etal. (1983a) Jetzer etal. (1983a) Galli and Leuenberger (1986) Leuenberger (1982) Leuenberger (1982) Leuenberger (1982) Jetzer etal. (1983a) Jetzer etal. (1983a) Jetzer etal. (1983a) Leuenberger (1982) Leuenberger (1982) Leuenberger (1982) Leuenberger (1982)

Leuenberger (1982) Jetzer etal. (1983a) Jetzer etal. (1983a) Jetzer etal. (1983b) Jetzer etal. (1983a)

Jetzer etal. (1983a) Jetzer etal. (1983a) Galli and Leuenberger (1986) Leuenberger and Rohera (1985) Leuenberger and Rohera (1985) Galli and Leuenberger (1986) Leuenberger and Rohera (1985) Leuenberger and Rohera (1985)

PEG, polyethylene glycol.

Hardness measurements on single crystals of pharmaceutical materials are sparse but where performed all have been carried out using a pyramidal indenter.

The earliest reported study on the hardness of pharmaceutical crystals was carried out by Ridgway etal. (1969a) using the Leitz microhardness tester with loads of 25 g or less. The crystals were mounted in heat-softened picene wax on a mounting slide to ensure that the surfaces were horizontal. It is interesting to note that the authors observed that aspirin and sucrose showed cracking and regarded this as a problem with the technique. Hardness values from this study are presented in Table 5. It is interesting to note that softer materials showed the most variation in results owing to a decline in the definition and quality of the indent.

The next reported study of crystal hardness using a Vickers hardness

Table 5 Indentation hardness measured on crystals

Indentation hardness

Table 5 Indentation hardness measured on crystals

Indentation hardness

Material

(MPa)

Reference

Sugars

a-Lactose monohydrate

523

Ichikawa etal. (1988)

Sucrose

645

Duncan-Hewitt and Weatherly (1989b)

Sucrose

636

Ridgway etal. (1969a)

Drugs

Paracetamol

421

Duncan-Hewitt and Weatherly (1989b)

Paracetamol

342

Ichikawa etal. (1988)

Sulfaphenazole

289

Ichikawa etal. (1988)

Hexamine

133

Ridgway etal. (1969a)

Hexamine

42

Ichikawa etal. (1988)

Sulfadimethoxine

231

Ichikawa etal. (1988)

Phenacetin

172

Ichikawa etal. (1988)

Salicylamide

151

Ridgway etal. (1969a)

Salicylamide

123

Ichikawa etal. (1988)

Aspirin

87

Ridgway etal. (1969a)

Alkali halides

NaCl

212

Ridgway etal. (1969a)

NaCl

213

Duncan-Hewitt and Weatherly (1989b)

NaCl

183

Ichikawa etal. (1988)

KC1

177

Ridgway etal. (1969a)

KC1

101

Ichikawa etal. (1988)

Others

Urea

91

Ridgway etal. (1969a)

Urea

83

Ichikawa etal. (1988)

tester was carried out 17 years later by Ichikawa etal. (1988). In this study the majority of the materials (with the exception of sucrose and urea) were recrystallized. Indentation was performed on the crystal face possessing the largest area, i.e. the face that grows the slowest during crystallization, as it was inferred that this face would have the greatest influence on the compaction properties. Ichikawa etal. (1988) attributed differences in crystal hardness as a reflection of the mechanism of deformation during compaction. They also showed that the reciprocal of crystal hardness correlated with the slope K from the Heckel equation (see later). Data reproduced in Table 5 represent the mean value from three different applied loads: 10 g, 25 g, 50 g. The importance of load on the indentation test should be noted as in the case of crystals the hardness generally decreases as load is increased and this is the exact opposite to that seen for compacts.

More recently Duncan-Hewitt and Weatherly (1989a, 1989b) measured the Vickers hardness on single crystals of a number of materials using a Leitz-Wetzlar Miniload tester with a load of 147 mN. It is interesting to note that the surfaces of sucrose were preconditioned, by washing with methanol then polishing by abrading with decreasing grades of emery paper. This may account for their higher hardness values compared with compacts (Table 4) as in this case the materials could be fully work-hardened solids. However, the authors did not indicate whether the other crystals were preconditioned. Furthermore Duncan-Hewitt and Weatherly (1989a) showed that the sucrose crystals were anisotropic in that different crystal faces gave different hardness values (Table 6) where the (001) and (100) are the predominant faces (i.e., have the largest area).

Finally, a brief mention must be made of the effects of dislocations on hardness, as crystallization can affect the number and distribution of these defects and therefore affect the resultant mechanical properties. In general, increasing the crystallization rate tends to increase the number of dislocations and therefore increase the indentation hardness. Such effects have

Table 6 The effect of crystal face on the indentation hardness of sucrose (Duncan-Hewitt and Weatherly, 1989a)

Crystal face

Hardness

(MPa)

001

636

100

649

110

642

010

649

been noted by Hiestand etal. (1981) and Wong and Aulton (1987) for ibuprofen and a-lactose monohydrate respectively.

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