Exploring the Relationship of Scratch Resistance, Hardness, and
other Physical Properties of Minerals using Mohs Scale Minerals
Donna L. Whitney
Annia K. Fayon
Margaret E. Broz
Geology & Geophysics, University of Minnesota, Minneapolis MN 55455
Robert F. Cook
National Institute for Standards and Technology, Gaithersburg, Maryland 20899
Geology & Geophysics, University of Minnesota, Minneapolis MN 55455
Chemical Engineering & Materials Science, University of Minnesota, Minneapolis
MN 55455
ABSTRACT
The Mohs scale is enshrined in geoscience curricula as a
simple and effective tool for identifying minerals and
understanding the influence of crystal structure and
chemistry on physical properties; e.g., hardness.
Measuring scratch resistance is different from measuring
hardness, however, because scratching involves
components of loading and shearing, whereas "absolute"
hardness is measured by the response of a material to
vertical loading (indentation). Although it is not practical
for most undergraduate classes to do indentation
hardness testing, students can evaluate tabulated
quantitative hardness data and compare these data with
their own determination of relative scratch resistance. To
help students better understand physical properties of
minerals, and in particular the concept of mineral
hardness, we present an example exercise based on
recent systematic measurements of the hardness of Mohs
scale minerals using indentation techniques. This
exercise allows students to explore the differences in
hardness among minerals of the Mohs scale, enhancing
their understanding of the Mohs scale itself as well as the
chemical and physical factors that influence mineral
hardness. The exercise is most appropriate for Earth
materials and mineralogy classes, but can be adapted for
students with different levels of expertise, including
introductory physical science students.
INTRODUCTION
Hardness is a physical property of minerals, and along
with other physical properties, such as cleavage, luster,
and streak, is commonly taught to geoscience students in
introductory physical geology, mineralogy, and other
classes involving Earth materials. Hardness is a function
of bonding strength (and therefore of crystal chemistry
and structure), so it is a useful property for
understanding the relationship between the structure
and composition of crystals and their macroscopic
properties. It is important that students have a basic
understanding of mineral physical properties such as
hardness, the relationship between physical properties
and crystal structure and chemistry, and the practical
applications of this knowledge (e.g., uses of minerals in
daily life).
In practice, hardness may also be understood as a
relative property: that is, students can determine by a
simple experiment ( Figure 1a) that calcite scratches more
easily than quartz, without necessarily quantifying that
relationship. When relative hardness is quantified, it is
by the Mohs scale of scratch resistance. Hardness as a
material property is measured by the response of a
material to loading ( Figure 1b), and can be described by
units of pressure (e.g., GigaPascals, GPa). Because
measured hardness values vary depending on the
56
technique, there is no absolute scale for hardness, and
relative scales such as the Mohs scale are therefore of
great practical value.
Mineralogy textbooks commonly equate hardness
with scratch resistance. For example, Klein (2002), p. 31:
"The resistance that a smooth surface of a mineral offers
to scratching is its hardness.."; and Perkins (2002), p. 55:
"Hardness is a mineral's resistance to abrasion or
scratching". It is also common for textbooks to contain a
graph of Mohs number vs. a quantity labeled "absolute"
hardness, although in some cases the measurement
methods and sources of the absolute hardness data are
not given (e.g., Klein, 2002, Figure 2.19, and Perkins,
2002, Figure 3.8a, both of which lack units; Nesse, 2000,
Figure 6.4, from an unknown source and method).
The text by Bloss (1994) correctly distinguishes
between Mohs hardness (scratch resistance) and
indentation hardness, and notes that each is a measure of
a mineral's resistance to "mechanical breakdown " (p.
357). A figure showing Mohs number vs. indentation
hardness measured by a variety of techniques (i.e.,
different indenter shapes, although these are not
described in the text; Figure 11-8) has units of kg/mm 2,
which can be approximately converted to GPa for
comparison with the present study by dividing the
values by 100.
As noted above, however, measured hardness depends
on the method used, so these "absolute" scales are not
very absolute. The most accurate explanation of
hardness involves a description of quantitative hardness
measurements by indentation methods in addition to
discussion of the concept of scratch resistance (e.g.,
Nesse, 2000, p. 99).
THE MOHS SCALE AND HARDNESS: AN
EXAMPLE EXERCISE
The main goal of this exercise is to give students a deeper
understanding of hardness. This is accomplished using
scratch-resistance experiments on mineral samples and
analysis of images and a dataset for indentation hardness
of the same minerals. The two parts of the exercise can be
done in any order.
Scratch Resistance - This part of the activity involves a
typical Mohs scale exercise in which students work with
the first 9 minerals of the Mohs scale: talc (1), gypsum (2),
calcite (3), fluorite (4), apatite (5), orthoclase (6), quartz
(7), topaz (8), corundum (9). The tenth mineral, diamond,
is typically excluded, although can of course be used if
the material is available. In our experiments, we tested
single crystals in addition to specimens from
commercially available Mohs testing kits for students,
and determined that some mineral samples in student
test kits (most notably talc) may be impure and give
variable results. For example, talc is commonly
intergrown with amphibole, which has a Mohs hardness
Journal of Geoscience Education, v. 55, n. 1, January, 2007, p. 56-61
Figure 1. Comparison of scratching (A) vs. indentation (B) as methods of testing the physical properties of
minerals. In indentation experiments, hardness is calculated from the load and the dimensions of the
indentation (2a).
of ~ 6, and talc is also strongly anisotropic with respect to
scratch resistance and hardness. If using such a kit, it is
important to test the talc to make sure that it can be
reliably scratched by fingernail (and, ideally, by a sharp
corner of a gypsum sample). Friedrich Mohs was aware
of the problem of talc impurity, and specified that
"Venetian talc" be used as the reference material (Mohs,
1825). Another possible problem with some student test
kits is the small size of the samples. For the most accurate
relative determination of scratch resistance, minerals
should have large, smooth surfaces available for
repeated testing.
We also recommend that, in addition to the official
Mohs minerals, other minerals be included in the
exercise for study after the Mohs reference materials
have been tested. Many of the Mohs scale minerals are
not common rock-forming minerals (e.g., apatite, topaz),
so it is useful to add minerals that students might
encounter in other parts of the class, in the field, or in
other courses. In the second part of the exercise, we use
hardness data for a non-Mohs mineral (in this example,
garnet) to test whether hardness can be used to predict
scratch resistance relative to Mohs scale minerals and
vice versa.
(H ~ 2-3 but varies depending on the person)), arrange
the samples in order and assign each a number, from
most easily scratched (1) to most difficult to scratch (9).
Be sure to examine carefully the scratches that you
produce, evaluating them for the ease with which you
made the scratch and the width and depth of the
scratches produced. You may also want to make multiple
scratches to try to reproduce your first result and to
evaluate whether scratch resistance varies on different
parts of the crystals. The best places to test a mineral are
smooth planes such as cleavage surfaces or crystal faces.
After you have placed the first 9 minerals in order of
their scratch resistance, test the additional mineral and
determine where it fits in the scale. The additional
mineral may have the same degree of scratch resistance
as one of your reference minerals or it may have an
intermediate value. If the latter, assign the mineral a
number such as 3.5, 6.5 etc., to show where it would fit on
the scale relative to the other minerals. (Note to instructor:
the "additional mineral" in this example is garnet, with a
Mohs number of approximately 7-8 depending on garnet
composition).
Questions:
Mohs Activity - Using the nine minerals and provided 1.
tools with known Mohs hardness (for example, a penny
(H =3), a glass plate (H = 5-6), and your own fingernails
Whitney et al. - Exploring the Physical Properties of Minerals
Was it easy to distinguish the minerals by scratch
resistance, or do some minerals have similar scratch
resistance, making the order difficult to determine
57
Figure 2. Contact impressions from microhardness experiments for the Mohs minerals, all at F = 2 N. (a) talc,
(b) gypsum, (c) calcite, (d) fluorite, (e) apatite, (f) orthoclase, (g) quartz, (h) topaz, (i) corundum.
for some samples? Whichever the case, explain your
answer with a sentence or two, giving examples.
Notes: If the mineral samples are end-members in
composition (i.e., lack impurities, inclusions, solid
solution components), in general it is not difficult to
determine the order of scratch resistance, although
some students may indicate some question about
minerals 3-7 depending on the quality of the samples
and the fingernail or other tools and minerals used 3.
for the testing. The instructor will need to evaluate
the range of appropriate answers in relation to the
materials used for testing.
2.
Did any mineral specimens vary in scratch resistance
when you tested different parts of the specimen?
Why or why not?
Notes: Again, the answer depends on the quality of your
mineral specimens (presence/absence of weathering
and impurities, single crystal specimens vs.
polycrystalline specimens, and size/smoothness of
planes tested). In theory, at least some minerals
should show detectable variation; e.g., different
cleavage planes of calcite, or gypsum scratched on
cleavage planes vs. across cleavage planes. Most
specimens, however, will not in practice show much
58
difference, although you can add a kyanite crystal
for a dramatic demonstration. We have not included
kyanite in this exercise because indentation
experiments produce extremely variable results,
particularly for the (001) plane. However, kyanite,
which is triclinic and therefore strongly anisotropic
in its properties, is useful for relating scratch
resistance to crystal structure.
No matter which answer you gave for #2, explain
why minerals might have physical properties that
vary with direction in a crystal. Discuss your answer
in the context of your answer to #2.
Notes: Physical properties such as hardness vary
with direction because bond strength varies in
different crystallographic directions depending on
the crystal structure of the mineral. In practice, these
differences might be too small to detect for some
minerals, at least using the testing methods in this
exercise. If some specimens used in this exercise
exhibit a distinction in scratch resistance with
direction and others (e.g., fluorite) do not, students
can discuss the relationship between less symmetric
and more symmetric structures on physical
properties. One possible approach for this question
is to have students fill out a chart of mineral
Journal of Geoscience Education, v. 55, n. 1, January, 2007, p. 56-61
Mohs Number
Mineral
Mineral Composition
Hardness (GPa)
1
2
3
4
5
6
7
8
9
10
Talc
Gypsum
Calcite
Fluorite
Apatite
Orthoclase
Quartz
Topaz
Corundum
Diamond
Mg3Si 4O10(OH)2
CaSO4·2H2O
CaCO3
CaF2
Ca5(PO4)3F
KAlSi3 O8
SiO2
Al2SiO4(OH, F)2
Al2O3
C
0.14 ± 0.03
0.61 ± 0.15
1.49 ± 0.11
1.85 ± 0.06
5.47 ± 0.82
6.87 ± 0.66
12.11 ± 1.14
12.85 ± 1.32
21.22 ± 0.03
(115*)
Uncertainties listed are one standard deviation.* Value from Novikov and Dub 1991
Mohs Number
Mineral
7-8
Garnet
Additional Data for Garnet
Mineral Composition
(Fe,Mg)3Al2 Si3O12
Hardness (GPa)
15.1 ± 1.20
Table 1. Indentation hardness of Mohs scale minerals.
Mohs Number
Mineral
a (contact ½
diagonal)*
1
2
3
4
5
6
7
8
9
Talc
Gypsum
Calcite
Fluorite
Apatite
Orthoclase
Quartz
Topaz
Corundum
77, 99**
41, 48**
28
23
13
13
9
9
7
* Measured in micrometers (µm) at 2N **Talc and gypsum have
variable behavior owing to their softness and anisotropy, as seen
in these two different measurements for the same material
measured under the same conditions.
Table 2. Measured contact diagonals from images of
indentations.
composition and structure (crystal system) in order
of increasing Mohs number, to provide more
information for discussing their answer.
(crystal faces, cleavage planes, or random orientations).
This is more easily detected with high-precision
microindentation experiments compared to macroscopic
scratch resistance tests. Indentation at particular loads
can also generate cracking at indentation corners (radial
cracks) and in other geometries (e.g., lateral cracks),
complicating analysis of images but providing
additional useful information about physical properties
such as fracture toughness.
In general, the simplest and clearest indentations are
generated in harder and/or high symmetry minerals as
compared to softer and lower symmetry minerals. For
example, in Figure 2, the clearest indentations are in
fluorite (low hardness but high symmetry isometric
crystal system), quartz (relatively hard mineral and high
symmetry hexagonal crystal system), topaz (low
symmetry orthorhombic crystal system but a hard
mineral), and corundum (a hard mineral with hexagonal
symmetry). In contrast, talc (soft, monoclinic), gypsum
(soft, monoclinic), calcite (soft, hexagonal), apatite
(medium hardness, hexagonal), and orthoclase (medium
hardness,
monoclinic)
have
combinations
of
low-moderate symmetry and low-moderate hardness
that produce variable indentation response and cracking.
The variation in talc and gypsum indentations can be
seen in the variation in length of contact diagonals
measured for two indentations of the same material
under the same conditions (2 Newtons) (Table 2).
Hardness - Hardness is most commonly measured in the
laboratory using indentation methods. An indenter,
typically a diamond, is applied to a sample at a known,
constant load, and then removed. Hardness can be Hardness Activity - Using the images in Figure 2
calculated from the dimensions of the residual (and/or the data in Table 2) and the equation H = F/2(a2),
indentation (Figure 2) by the equation:
calculate hardness values for the minerals given
(multiply the result by 1000 to get the correct unit, GPa).
H = F/2(a2),
Graph the results against Mohs number, adding the
literature value for diamond if desired (Table 1). Plot
where H is hardness (typically in units of GPa), F is the Mohs number on the x-axis and hardness on the y-axis.
applied load (measured in Newtons, N), and a is half of (Note to instructor: Results shown in Figure 3. You can also
the diagonal length of the indentation (measured in ask the students to plot log(H) against Mohs number).
micrometers, µm). If F is given and a is either given or
measured from an image of the indentation ( Figure 2), H Questions:
can be determined (Table 1).
All minerals, even isotropic ones, exhibit variable 1. Does hardness vary in a systematic or linear way
bond strength in different directions and therefore
with respect to Mohs number? Explain your answer
exhibit different indentation response on different planes
with reference to the graph you produced.
Whitney et al. - Exploring the Physical Properties of Minerals
59
estimated Mohs number compare with the
prediction from your graph?). What does this new
information indicate about the relationship between
hardness and the Mohs scale?
Figure 3. Graph of Mohs numbers vs. hardness
calculated from indentation testing. This graph was 5.
constructed using the data in Table 1 (open circles)
and hardness calculated using the values for a
(contact diagonal) in Table 2 (closed circles). The
latter are more similar to results that would be
obtained by students using images to measure the
indentation dimensions.
Notes: The relationship is not linear and has some
gaps (although the gaps aren't large), and the overall
trend is of increasing Mohs number with indentation
hardness. If students plot log(H) vs. Mohs number,
the trend is more linear, but not completely, and
there are still gaps of varying magnitude between
values for adjacent minerals on the Mohs scale.
2.
3.
4.
60
Notes: Garnet has a Mohs number of 7-8. These
numbers are approximately what you would predict
from the indentation hardness, although perhaps
slightly too low. In general, though, this one example
suggests that the relationship between hardness and
scratch resistance is systematic enough to allow
estimation of one value from the other. Note,
however, that garnet hardness depends on garnet
composition (e.g., Mg-rich garnet is much harder
than Ca-rich garnet ), so depending on what sample
you use, garnet will either be similar in hardness to
quartz (12 GPa) or harder (15 GPa) (Whitney et al., in
press). We therefore recommend that you use a
common red-purple Fe-Mg garnet in this exercise to
obtain a result that falls between quartz and topaz or
that corresponds to the scratch resistance of topaz.
Discuss the hardness data and the images in Figure 2
in relation to the crystal systems of the minerals. For
example, compare the hardness and indentation
response of low symmetry minerals with high
symmetry minerals, and compare the properties of
minerals with the same crystal system (e.g., fluorite
and diamond are both isometric/cubic; talc,
gypsum, and orthoclase are all monoclinic; calcite,
apatite, quartz, and corundum are all hexagonal).
Also consider other factors, such as crystal chemistry
and the presence or absence of cleavage, and discuss
what you think the most important factors are for
predicting a mineral's hardness. This question also
relates to #3 in the Mohs activity.
Synthesis Question for Both Activities - Give
Are there any minerals with different Mohs numbers examples from daily life or other examples from science,
but the same indentation hardness? Refer to the industry, medicine, or other applications in which the
hardness and scratch resistance of a material is
Mohs minerals specifically in your answer.
important.
Notes: Quartz and topaz have essentially the same
Example answers: The general theme of this thought
absolute hardness, ~ 12 GPa, but quartz is Mohs
exercise is any case in daily life in which sharp
number 7 and topaz is Mohs number 8.
contact takes place, especially if it's a moving contact.
Students could mention common activities such as
Do you think that scratch resistance (as measured by
using sandpaper or other abrasives to smooth or
Mohs number) and hardness (as calculated from
clean surfaces, or could note that you don't want to
indentation experiments) are essentially the same
chew anything with a hardness greater than that of
thing or are they significantly different properties?
apatite (if you want to keep your teeth). In addition,
Discuss with reference to your results and graph.
hardness and scratch resistance are important for
determining what materials will be used in coins,
Notes: The fact that quartz and topaz have the same
vehicles, building materials, farm implements, and
hardness but different scratch resistance suggests
so on. In geology, the hardness of minerals is
that these properties are different and that factors
important for understanding how they deform; e.g.,
other than hardness influence scratch resistance. On
brittle fracture of minerals in an earthquake.
the other hand, the properties are to some extent
related or there wouldn't be as much correlation as
there is, so there is a range of possible answers to this
question. The next question explores this concept ASSESSMENT
further.
This exercise has a range of goals related to
If you were told that a mineral has a hardness of 15 understanding discipline-centered concepts and
GPa, what would you predict its Mohs number development of critical reasoning skills. General aims of
would be (approximately)? Garnet has a hardness of the exercise include
15 GPa - look up its Mohs number and compare the
results to your estimate. (Or, if you tested garnet in • conducting experiments (scratch testing) that are
reproducible and that are the basis for analysis,
the other part of the exercise, how does your
Journal of Geoscience Education, v. 55, n. 1, January, 2007, p. 56-61
• organizing and analyzing data, including creating and
interpreting a graph and using tabulated data and
images,
• developing critical reasoning skills related to two
datasets that can be compared, resulting in a deeper
understanding of fundamental concepts,
• seeing applications of the concepts to daily life and
academic subjects.
The last aim may involve a change in perception by
students in the course of the exercise. That is, students
may not initially see why knowing about the physical
properties of minerals has relevance to their lives and
other classes, but they will discover and learn examples
that they can relate to other life and academic
experiences.
More specialized goals of the exercise include
SUMMARY
Hardness and scratch resistance tests are excellent
teaching tools because they are simple, visual, easily
reproduced, and involve comparison of minerals. These
properties are also good examples upon which to base
discussion of links between crystal chemistry, crystal
structure, bond types/strengths, and macroscopic
properties. The involvement in this exercise of a
quantitative dataset for mineral hardness introduces
students to an important modern technique for
measuring mineral properties, one that has widespread
use in materials science and engineering, as well as use
and applications in mineralogy, mineral physics,
structural geology, and seismology.
ACKNOWLEDGEMENTS
The indentation experiments were funded by NSF grant
• relating physical properties of minerals to crystal EAR-010667 to D.L. Whitney, were conducted in the
chemistry and structure,
laboratory of R.F. Cook at the University of Minnesota,
concepts,
Brandon Schwab, an anonymous reviewer, and associate
• understanding specific scientific applications of the and comprise the M.S. thesis of M.E. Broz. We thank
• increasing student familiarity with common minerals editor Johnson for very helpful reviews.
and their composition and structure (crystal systems,
cleavage planes).
REFERENCES
Data that can be used to assess student learning include Bloss, F.D., 1994, Crystallography and Crystal
Chemistry, Mineralogical Society of America, 545 p.
• the accuracy of student-produced graphs of Mohs Broz, M.E., Cook, R.F., and Whitney, D.L., 2006,
number vs. indentation hardness, and
Microhardness, toughness, and modulus of Mohs
• answers to the questions posed - both technical
scale minerals, American Mineralogist, v. 91, p.
questions directly related to the experiments and data,
135-142.
as well as more general questions about underlying Klein, C., 2002, Manual of Mineral Science, 22nd edition,
concepts and applications.
John Wiley and Sons, 642 p.
Mohs, F., 1825, Treatise on Mineralogy, (translated by W.
The overall effectiveness of the exercise can be
Haidinger). Caledonian Mercury Press, Edinburgh,
evaluated by student grades on the exercise and by
458 p.
completion rates of the exercise. If students are asked Nesse, W.D., 2000, Introduction to Mineralogy, Oxford
both before and after the exercise about their knowledge
University Press, 442 p.
and views of uses of minerals and mineral properties, Novikov, N.V., and Dub, S.N., 1991, Fracture toughness
one can also evaluate changes in perception regarding
of diamond single crystals, Journal of Hard
the significance and general applications of mineral
Materials, v. 2, p. 3-11.
properties beyond a classroom activity. A further Perkins, D., 2002, Mineralogy, 2nd edition. Prentice-Hall,
indication of success of the exercise is the degree to
483 p.
which student understanding of the related concepts of Whitne, D.L., Broz, M.E., and Cook, R.F., (in press),
mineral structure, composition, and properties is
Hardness, fracture toughness, and elastic modulus
enhanced, and the extent of transfer of knowledge to
of some common metamorphic minerals, American
other classes that involve properties of minerals.
Mineralogist.
Whitney et al. - Exploring the Physical Properties of Minerals
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