ABSTRACT

The Mohs scale is enshrined in geoscience curricula as asimple and effective tool for identifying minerals andunderstanding the influence of crystal structure andchemistry on physical properties; e.g., hardness.Measuring scratch resistance is different from measuringhardness, however, because scratching involvescomponents of loading and shearing, whereas "absolute" hardness is measured by the response of a material tovertical loading (indentation). Although it is not practicalfor most undergraduate classes to do indentationhardness testing, students can evaluate tabulatedquantitative hardness data and compare these data withtheir own determination of relative scratch resistance. Tohelp students better understand physical properties ofminerals, and in particular the concept of mineralhardness, we present an example exercise based onrecent systematic measurements of the hardness of Mohsscale minerals using indentation techniques. Thisexercise allows students to explore the differences inhardness among minerals of the Mohs scale, enhancingtheir understanding of the Mohs scale itself as well as thechemical and physical factors that influence mineralhardness. The exercise is most appropriate for Earthmaterials and mineralogy classes, but can be adapted forstudents with different levels of expertise, includingintroductory physical science students.

INTRODUCTION

Hardness is a physical property of minerals, and alongwith other physical properties, such as cleavage, luster,and streak, is commonly taught to geoscience students inintroductory physical geology, mineralogy, and otherclasses involving Earth materials. Hardness is a functionof bonding strength (and therefore of crystal chemistryand structure), so it is a useful property forunderstanding the relationship between the structureand composition of crystals and their macroscopicproperties. It is important that students have a basicunderstanding of mineral physical properties such ashardness, the relationship between physical propertiesand crystal structure and chemistry, and the practicalapplications of this knowledge (e.g., uses of minerals indaily life).

In practice, hardness may also be understood as arelative property: that is, students can determine by asimple experiment ( Figure 1a) that calcite scratches moreeasily than quartz, without necessarily quantifying thatrelationship. When relative hardness is quantified, it isby the Mohs scale of scratch resistance. Hardness as amaterial property is measured by the response of amaterial to loading ( Figure 1b), and can be described byunits of pressure (e.g., GigaPascals, GPa). Becausemeasured hardness values vary depending on the

technique, there is no absolute scale for hardness, andrelative scales such as the Mohs scale are therefore ofgreat practical value.

Mineralogy textbooks commonly equate hardnesswith scratch resistance. For example, Klein (2002), p. 31:"The resistance that a smooth surface of a mineral offersto scratching is its hardness.."; and Perkins (2002), p. 55:"Hardness is a mineral's resistance to abrasion orscratching". It is also common for textbooks to contain agraph of Mohs number vs. a quantity labeled "absolute"hardness, although in some cases the measurementmethods and sources of the absolute hardness data arenot 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 distinguishesbetween Mohs hardness (scratch resistance) andindentation hardness, and notes that each is a measure ofa mineral's resistance to "mechanical breakdown " (p.357). A figure showing Mohs number vs. indentationhardness measured by a variety of techniques (i.e.,different indenter shapes, although these are notdescribed in the text; Figure 11-8) has units of kg/mm2,which can be approximately converted to GPa forcomparison with the present study by dividing thevalues by 100.As noted above, however, measured hardness dependson the method used, so these "absolute" scales are notvery absolute. The most accurate explanation ofhardness involves a description of quantitative hardnessmeasurements by indentation methods in addition todiscussion of the concept of scratch resistance (e.g.,Nesse, 2000, p. 99).

THE MOHS SCALE AND HARDNESS: ANEXAMPLE EXERCISE

The main goal of this exercise is to give students a deeperunderstanding of hardness. This is accomplished usingscratch-resistance experiments on mineral samples andanalysis of images and a dataset for indentation hardnessof the same minerals. The two parts of the exercise can bedone in any order.

Scratch Resistance - This part of the activity involves atypical Mohs scale exercise in which students work withthe 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 ifthe material is available. In our experiments, we testedsingle crystals in addition to specimens fromcommercially available Mohs testing kits for students,and determined that some mineral samples in studenttest kits (most notably talc) may be impure and givevariable results. For example, talc is commonlyintergrown with amphibole, which has a Mohs hardness

56 Journal of Geoscience Education, v. 55, n. 1, January, 2007, p. 56-61

Exploring the Relationship of Scratch Resistance, Hardness, andother Physical Properties of Minerals using Mohs Scale Minerals

Donna L. Whitney Geology & Geophysics, University of Minnesota, Minneapolis MN 55455

Annia K. Fayon Geology & Geophysics, University of Minnesota, Minneapolis MN 55455

Margaret E. Broz Chemical Engineering & Materials Science, University of Minnesota, Minneapolis MN 55455

Robert F. Cook National Institute for Standards and Technology, Gaithersburg, Maryland 20899

of ~ 6, and talc is also strongly anisotropic with respect toscratch resistance and hardness. If using such a kit, it isimportant to test the talc to make sure that it can bereliably scratched by fingernail (and, ideally, by a sharpcorner of a gypsum sample). Friedrich Mohs was awareof the problem of talc impurity, and specified that"Venetian talc" be used as the reference material (Mohs,1825). Another possible problem with some student testkits is the small size of the samples. For the most accuraterelative determination of scratch resistance, mineralsshould have large, smooth surfaces available forrepeated testing.

We also recommend that, in addition to the officialMohs minerals, other minerals be included in theexercise for study after the Mohs reference materialshave been tested. Many of the Mohs scale minerals arenot common rock-forming minerals (e.g., apatite, topaz),so it is useful to add minerals that students mightencounter in other parts of the class, in the field, or inother courses. In the second part of the exercise, we usehardness data for a non-Mohs mineral (in this example,garnet) to test whether hardness can be used to predictscratch resistance relative to Mohs scale minerals andvice versa.

Mohs Activity - Using the nine minerals and providedtools with known Mohs hardness (for example, a penny(H =3), a glass plate (H = 5-6), and your own fingernails

(H ~ 2-3 but varies depending on the person)), arrangethe samples in order and assign each a number, frommost easily scratched (1) to most difficult to scratch (9).Be sure to examine carefully the scratches that youproduce, evaluating them for the ease with which youmade the scratch and the width and depth of thescratches produced. You may also want to make multiplescratches to try to reproduce your first result and toevaluate whether scratch resistance varies on differentparts of the crystals. The best places to test a mineral aresmooth planes such as cleavage surfaces or crystal faces.

After you have placed the first 9 minerals in order oftheir scratch resistance, test the additional mineral anddetermine where it fits in the scale. The additionalmineral may have the same degree of scratch resistanceas one of your reference minerals or it may have anintermediate value. If the latter, assign the mineral anumber such as 3.5, 6.5 etc., to show where it would fit onthe scale relative to the other minerals. (Note to instructor:the "additional mineral" in this example is garnet, with aMohs number of approximately 7-8 depending on garnetcomposition).

Questions:

1. Was it easy to distinguish the minerals by scratchresistance, or do some minerals have similar scratchresistance, making the order difficult to determine

Whitney et al. - Exploring the Physical Properties of Minerals 57

Figure 1. Comparison of scratching (A) vs. indentation (B) as methods of testing the physical properties ofminerals. In indentation experiments, hardness is calculated from the load and the dimensions of theindentation (2a).

for some samples? Whichever the case, explain youranswer with a sentence or two, giving examples.

Notes: If the mineral samples are end-members incomposition (i.e., lack impurities, inclusions, solidsolution components), in general it is not difficult todetermine the order of scratch resistance, althoughsome students may indicate some question aboutminerals 3-7 depending on the quality of the samples and the fingernail or other tools and minerals usedfor the testing. The instructor will need to evaluatethe range of appropriate answers in relation to thematerials used for testing.

2. Did any mineral specimens vary in scratch resistancewhen you tested different parts of the specimen?Why or why not?

Notes: Again, the answer depends on the quality of yourmineral specimens (presence/absence of weatheringand impurities, single crystal specimens vs.polycrystalline specimens, and size/smoothness ofplanes tested). In theory, at least some mineralsshould show detectable variation; e.g., differentcleavage planes of calcite, or gypsum scratched oncleavage planes vs. across cleavage planes. Mostspecimens, however, will not in practice show much

difference, although you can add a kyanite crystalfor a dramatic demonstration. We have not includedkyanite in this exercise because indentationexperiments produce extremely variable results,particularly for the (001) plane. However, kyanite,which is triclinic and therefore strongly anisotropicin its properties, is useful for relating scratchresistance to crystal structure.

3. No matter which answer you gave for #2, explainwhy minerals might have physical properties thatvary with direction in a crystal. Discuss your answerin the context of your answer to #2.

Notes: Physical properties such as hardness varywith direction because bond strength varies indifferent crystallographic directions depending onthe crystal structure of the mineral. In practice, thesedifferences might be too small to detect for someminerals, at least using the testing methods in thisexercise. If some specimens used in this exerciseexhibit a distinction in scratch resistance withdirection and others (e.g., fluorite) do not, studentscan discuss the relationship between less symmetricand more symmetric structures on physicalproperties. One possible approach for this questionis to have students fill out a chart of mineral

58 Journal of Geoscience Education, v. 55, n. 1, January, 2007, p. 56-61

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.

composition and structure (crystal system) in orderof increasing Mohs number, to provide moreinformation for discussing their answer.

Hardness - Hardness is most commonly measured in thelaboratory using indentation methods. An indenter,typically a diamond, is applied to a sample at a known,constant load, and then removed. Hardness can becalculated from the dimensions of the residualindentation (Figure 2) by the equation:

H = F/2(a2),

where H is hardness (typically in units of GPa), F is theapplied load (measured in Newtons, N), and a is half ofthe diagonal length of the indentation (measured inmicrometers, µm). If F is given and a is either given ormeasured from an image of the indentation ( Figure 2), Hcan be determined (Table 1).

All minerals, even isotropic ones, exhibit variablebond strength in different directions and thereforeexhibit different indentation response on different planes

(crystal faces, cleavage planes, or random orientations).This is more easily detected with high-precisionmicroindentation experiments compared to macroscopicscratch resistance tests. Indentation at particular loadscan also generate cracking at indentation corners (radialcracks) and in other geometries (e.g., lateral cracks),complicating analysis of images but providingadditional useful information about physical propertiessuch as fracture toughness.

In general, the simplest and clearest indentations aregenerated in harder and/or high symmetry minerals ascompared to softer and lower symmetry minerals. Forexample, in Figure 2, the clearest indentations are influorite (low hardness but high symmetry isometriccrystal system), quartz (relatively hard mineral and highsymmetry hexagonal crystal system), topaz (lowsymmetry orthorhombic crystal system but a hardmineral), and corundum (a hard mineral with hexagonalsymmetry). In contrast, talc (soft, monoclinic), gypsum(soft, monoclinic), calcite (soft, hexagonal), apatite(medium hardness, hexagonal), and orthoclase (medium hardness, monoclinic) have combinations oflow-moderate symmetry and low-moderate hardnessthat produce variable indentation response and cracking.The variation in talc and gypsum indentations can beseen in the variation in length of contact diagonalsmeasured for two indentations of the same materialunder the same conditions (2 Newtons) (Table 2).

Hardness Activity - Using the images in Figure 2(and/or the data in Table 2) and the equation H = F/2(a2),calculate hardness values for the minerals given(multiply the result by 1000 to get the correct unit, GPa).Graph the results against Mohs number, adding theliterature value for diamond if desired (Table 1). PlotMohs number on the x-axis and hardness on the y-axis.(Note to instructor: Results shown in Figure 3. You can alsoask the students to plot log(H) against Mohs number).

Questions:

1. Does hardness vary in a systematic or linear waywith respect to Mohs number? Explain your answerwith reference to the graph you produced.

Whitney et al. - Exploring the Physical Properties of Minerals 59

Mohs Number Mineral Mineral Composition Hardness (GPa)

1 Talc Mg3Si4O10(OH)2 0.14 ± 0.03

2 Gypsum CaSO4·2H2O 0.61 ± 0.15

3 Calcite CaCO3 1.49 ± 0.11

4 Fluorite CaF2 1.85 ± 0.06

5 Apatite Ca5(PO4)3F 5.47 ± 0.82

6 Orthoclase KAlSi3O8 6.87 ± 0.66

7 Quartz SiO2 12.11 ± 1.14

8 Topaz Al2SiO4(OH, F)2 12.85 ± 1.32

9 Corundum Al2O3 21.22 ± 0.03

10 Diamond C (115*)

Uncertainties listed are one standard deviation.* Value from Novikov and Dub 1991

Additional Data for Garnet

Mohs Number Mineral Mineral Composition Hardness (GPa)

7-8 Garnet (Fe,Mg)3Al2Si3O12 15.1 ± 1.20

Table 1. Indentation hardness of Mohs scale minerals.

Mohs Number Mineral a (contact ½diagonal)*

1 Talc 77, 99**

2 Gypsum 41, 48**

3 Calcite 28

4 Fluorite 23

5 Apatite 13

6 Orthoclase 13

7 Quartz 9

8 Topaz 9

9 Corundum 7

* Measured in micrometers (µm) at 2N **Talc and gypsum havevariable behavior owing to their softness and anisotropy, as seenin these two different measurements for the same materialmeasured under the same conditions.

Table 2. Measured contact diagonals from images ofindentations.

Notes: The relationship is not linear and has somegaps (although the gaps aren't large), and the overalltrend is of increasing Mohs number with indentationhardness. If students plot log(H) vs. Mohs number,the trend is more linear, but not completely, andthere are still gaps of varying magnitude betweenvalues for adjacent minerals on the Mohs scale.

2. Are there any minerals with different Mohs numbersbut the same indentation hardness? Refer to theMohs minerals specifically in your answer.

Notes: Quartz and topaz have essentially the sameabsolute hardness, ~ 12 GPa, but quartz is Mohsnumber 7 and topaz is Mohs number 8.

3. Do you think that scratch resistance (as measured byMohs number) and hardness (as calculated fromindentation experiments) are essentially the samething or are they significantly different properties?Discuss with reference to your results and graph.

Notes: The fact that quartz and topaz have the samehardness but different scratch resistance suggeststhat these properties are different and that factorsother than hardness influence scratch resistance. Onthe other hand, the properties are to some extentrelated or there wouldn't be as much correlation asthere is, so there is a range of possible answers to thisquestion. The next question explores this conceptfurther.

4. If you were told that a mineral has a hardness of 15GPa, what would you predict its Mohs numberwould be (approximately)? Garnet has a hardness of15 GPa - look up its Mohs number and compare theresults to your estimate. (Or, if you tested garnet inthe other part of the exercise, how does your

estimated Mohs number compare with theprediction from your graph?). What does this newinformation indicate about the relationship betweenhardness and the Mohs scale?

Notes: Garnet has a Mohs number of 7-8. Thesenumbers are approximately what you would predictfrom the indentation hardness, although perhapsslightly too low. In general, though, this one examplesuggests that the relationship between hardness andscratch resistance is systematic enough to allowestimation of one value from the other. Note,however, that garnet hardness depends on garnetcomposition (e.g., Mg-rich garnet is much harderthan Ca-rich garnet ), so depending on what sampleyou use, garnet will either be similar in hardness toquartz (12 GPa) or harder (15 GPa) (Whitney et al., inpress). We therefore recommend that you use acommon red-purple Fe-Mg garnet in this exercise toobtain a result that falls between quartz and topaz orthat corresponds to the scratch resistance of topaz.

5. Discuss the hardness data and the images in Figure 2in relation to the crystal systems of the minerals. Forexample, compare the hardness and indentationresponse of low symmetry minerals with highsymmetry minerals, and compare the properties ofminerals with the same crystal system (e.g., fluoriteand 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 discusswhat you think the most important factors are forpredicting a mineral's hardness. This question alsorelates to #3 in the Mohs activity.

Synthesis Question for Both Activities - Giveexamples from daily life or other examples from science,industry, medicine, or other applications in which thehardness and scratch resistance of a material isimportant.

Example answers: The general theme of this thoughtexercise is any case in daily life in which sharpcontact takes place, especially if it's a moving contact.Students could mention common activities such asusing sandpaper or other abrasives to smooth orclean surfaces, or could note that you don't want tochew anything with a hardness greater than that ofapatite (if you want to keep your teeth). In addition,hardness and scratch resistance are important fordetermining what materials will be used in coins,vehicles, building materials, farm implements, andso on. In geology, the hardness of minerals isimportant for understanding how they deform; e.g.,brittle fracture of minerals in an earthquake.

ASSESSMENT

This exercise has a range of goals related tounderstanding discipline-centered concepts anddevelopment of critical reasoning skills. General aims ofthe exercise include

• conducting experiments (scratch testing) that arereproducible and that are the basis for analysis,

60 Journal of Geoscience Education, v. 55, n. 1, January, 2007, p. 56-61

Figure 3. Graph of Mohs numbers vs. hardnesscalculated from indentation testing. This graph wasconstructed using the data in Table 1 (open circles)and hardness calculated using the values for a

(contact diagonal) in Table 2 (closed circles). Thelatter are more similar to results that would beobtained by students using images to measure theindentation dimensions.

• organizing and analyzing data, including creating andinterpreting a graph and using tabulated data andimages,

• developing critical reasoning skills related to twodatasets that can be compared, resulting in a deeperunderstanding of fundamental concepts,

• seeing applications of the concepts to daily life andacademic subjects.

The last aim may involve a change in perception bystudents in the course of the exercise. That is, studentsmay not initially see why knowing about the physicalproperties of minerals has relevance to their lives andother classes, but they will discover and learn examplesthat they can relate to other life and academicexperiences.

More specialized goals of the exercise include

• relating physical properties of minerals to crystalchemistry and structure,

• understanding specific scientific applications of theconcepts,

• increasing student familiarity with common mineralsand their composition and structure (crystal systems,cleavage planes).

Data that can be used to assess student learning include

• the accuracy of student-produced graphs of Mohsnumber vs. indentation hardness, and

• answers to the questions posed - both technicalquestions directly related to the experiments and data,as well as more general questions about underlyingconcepts and applications.

The overall effectiveness of the exercise can beevaluated by student grades on the exercise and bycompletion rates of the exercise. If students are askedboth before and after the exercise about their knowledgeand views of uses of minerals and mineral properties,one can also evaluate changes in perception regardingthe significance and general applications of mineralproperties beyond a classroom activity. A furtherindication of success of the exercise is the degree towhich student understanding of the related concepts ofmineral structure, composition, and properties isenhanced, and the extent of transfer of knowledge toother classes that involve properties of minerals.

SUMMARY

Hardness and scratch resistance tests are excellentteaching tools because they are simple, visual, easilyreproduced, and involve comparison of minerals. Theseproperties are also good examples upon which to basediscussion of links between crystal chemistry, crystalstructure, bond types/strengths, and macroscopicproperties. The involvement in this exercise of aquantitative dataset for mineral hardness introducesstudents to an important modern technique formeasuring mineral properties, one that has widespreaduse in materials science and engineering, as well as useand applications in mineralogy, mineral physics,structural geology, and seismology.

ACKNOWLEDGEMENTS

The indentation experiments were funded by NSF grantEAR-010667 to D.L. Whitney, were conducted in thelaboratory of R.F. Cook at the University of Minnesota,and comprise the M.S. thesis of M.E. Broz. We thankBrandon Schwab, an anonymous reviewer, and associateeditor Johnson for very helpful reviews.

REFERENCES

Bloss, F.D., 1994, Crystallography and CrystalChemistry, Mineralogical Society of America, 545 p.

Broz, M.E., Cook, R.F., and Whitney, D.L., 2006,Microhardness, toughness, and modulus of Mohsscale minerals, American Mineralogist, v. 91, p.135-142.

Klein, C., 2002, Manual of Mineral Science, 22nd edition,John Wiley and Sons, 642 p.

Mohs, F., 1825, Treatise on Mineralogy, (translated by W.Haidinger). Caledonian Mercury Press, Edinburgh,458 p.

Nesse, W.D., 2000, Introduction to Mineralogy, OxfordUniversity Press, 442 p.

Novikov, N.V., and Dub, S.N., 1991, Fracture toughnessof diamond single crystals, Journal of HardMaterials, v. 2, p. 3-11.

Perkins, D., 2002, Mineralogy, 2nd edition. Prentice-Hall,483 p.

Whitne, D.L., Broz, M.E., and Cook, R.F., (in press),Hardness, fracture toughness, and elastic modulusof some common metamorphic minerals, AmericanMineralogist.

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