micromachines

Review Low Temperature Nanoindentation: Development and Applications

Shunbo Wang 1 and Hongwei Zhao 1,2,*

1 School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China; [email protected] 2 Key Laboratory of CNC Equipment Reliability, Ministry of Education, Changchun 130025, China * Correspondence: [email protected]; Tel.: +86-0431-85095757



Received: 15 March 2020; Accepted: 30 March 2020; Published: 13 April 2020


Abstract: Nanoindentation technique at low temperatures have developed from initial micro-hardness driving method at a single temperature to modern depth-sensing indentation (DSI) method with variable temperatures over the last three decades. The technique and implementation of representative cooling systems adopted on the indentation apparatuses are discussed in detail here, with particular emphasis on pros and cons of combination with indentation technique. To obtain accurate nanoindentation curves and calculated results of material properties, several influence factors have been carefully considered and eliminated, including thermal drift and temperature induced influence on indenter and specimen. Finally, we further show some applications on typical materials and discuss the perspectives related to low temperature nanoindentation technique.

Keywords: low temperature; nanoindentation; hardness test; apparatus; mechanical properties

1. Introduction Nanoindentation technique has become one of the most popular mechanical property testing methods in recent years [1–5]. Compared with uniaxial tension and compression tests, the specimen requirements of nanoindentation were more simplified: a flat, no shape required surface. The mechanical properties, including but not limited to hardness and elastic modulus, can be obtained automatically via commercial system using Hertz contact theory [6] and Oliver-Pharr analysis method [7]. Moreover, selectable micro-region and huge testing amount on the single specimen provides significant advantages of nanoindentation over other macro-mechanical tests. Mechanical properties of each component of the specimen can be studied separately in details, as well as the interaction between them [8,9]. The negligible testing area of nanoindentation is also in favor of high throughput test and testing on small-scale materials, such as films and particles [10,11]. With attaching low temperature environment on the conventional nanoindentation system, materials can be investigated at service temperatures and conditions relevant to industrial applications via nanoindentation method. Scientifically, low temperature nanoindentation technique is attractive to academic researchers for its combination low temperature environment to convenient nanoindentation method. The researchable aspects are not only limited to variation of specific mechanical parameters with temperature decreasing, while high hydrostatic pressure, shear stress, and local strain can be easily realized via nanoindentation method [12–14]. Interesting phenomena caused by such reasons are also strongly associated with the variation of temperature. Combining with subsequent testing analysis procedures on residual impressions, such as focused ion beam (FIB), scanning electron microscope (SEM), and transmission electron microscope (TEM) methods, the complex evolvement caused by nanoindentation at low temperatures can be observed intuitively [15–18].

Micromachines 2020, 11, 407; doi:10.3390/mi11040407 www.mdpi.com/journal/micromachines Micromachines 2020, 11, x 2 of 25 complex evolvement caused by nanoindentation at low temperatures can be observed intuitively [15– Micromachines 2020, 11, 407 2 of 25 18]. Low temperature nanoindentation has developed in nearly the past three decades. However, the investigationsLow temperature on such nanoindentation field are not hasas much developed as high innearly temperature the past nanoindentation three decades. However, [19–23] and the relevantinvestigations commercial on such system field are was not asrelatively much as highrare. temperatureCompared nanoindentationwith various and [19 flexible–23] and ways relevant of applicationcommercial of system in a high was temperature relatively rare. environment, Compared including with various resistance and flexible and laser ways heating, of application basically of allin athe high cooling temperature sources environment,in low temperature including nanoindentation resistance and system laser heating, are cryogenic basically liquids, all the such cooling as liquidsources nitrogen in low temperature(LN2) and liquid nanoindentation helium (LHe) system[24–27]. are Academic cryogenic designers liquids, are such always as liquid dedicated nitrogen to solving(LN2) and the liquiddifficulties helium in applying (LHe) [24 a –low27]. temper Academicature designersenvironment are on always a nanoindentation dedicated to system solving and the retainingdifficulties the in high applying sensitivity a low temperatureand accuracy environment of nanoindentation on a nanoindentation technique. system and retaining the highIn sensitivity this article, and the accuracy methods of and nanoindentation testing theories technique. of indentation at ambient and low temperature, includingIn this micro-hardness article, the methods testing and and testing nanoindentation theories of indentation testing, are at introduced. ambient and Several low temperature, stages of nanoindentationincluding micro-hardness systems capable testing of and testing nanoindentation at low temperatures testing, are discussed introduced. in detail. Several The stages major of designnanoindentation elements systemsfeatured capable in the ofsystems testing atare low de temperaturesscribed in relation are discussed to their in low detail. temperature The major functionality.design elements Influence featured factors in the systemsleading areto describedmeasurement in relation error, toincluding their low contact temperature thermal functionality. drift and variationInfluence of factors testing leading system to measurementitself under a error,low temp includingerature contact environment, thermal driftare also and presented. variation of Current testing applicationsystem itself status under of a lowlow temperature temperature environment, indentation aretechnique also presented. is introduced Current in application testing materials status of respects:low temperature metallic indentation materials, techniquesemiconductor is introduced materials, in testingand ceramic materials materials. respects: A metallicsummary materials, of the developmentsemiconductor on materials, low temperature and ceramic nanoindentation materials. A summarytechniques of and the developmentperspectives of on the low technique temperature are concluded.nanoindentation techniques and perspectives of the technique are concluded.

2. Methods Methods of of Indentation Indentation Ever since people found found the the mechanical mechanical properties properties of of material material can can be be investigated investigated artificially, artificially, differentdifferent kinds kinds of of testing testing methods methods have have been been develo developedped through through destroying destroying the the original original structure structure of theof thespecimen. specimen. An impression An impression can be can obtained be obtained on the onsurface the surface of one material of one material permanently permanently by another by sharpanother object sharp through object through a certain a contacting certain contacting load. The load. size The of sizethe impression of the impression was logically was logically related related with thewith “hardness” the “hardness” of the of theimpressed impressed material, material, which which became became the the origin origin of of the the modern modern indentation technique.technique. InIn thisthis section, section, we we will will introduce introduce working working principles principles of two diofff erenttwo indentationdifferent indentation techniques, techniques,micro-hardness micro-hardness and nanoindentation, and nanoindentation, which are widely which applied are widely in academic applied research, in academic and analysis research, of andthe twoanalysis techniques, of the two respectively, techniques, will respectively, be discussed. will be discussed.

2.1. Micro-Hardness Micro-Hardness Testing Testing A representative system of of micro-hardness micro-hardness test test is is shown shown in in Figure Figure 11a,a, containing electric motor, loadload sensor,sensor, indenter,indenter, and and optical optical microscope. microscope. During During an indentationan indentation process, process, the electric the electric motor motor drives drivesthe indenter the indenter moving moving down alongdown zalong axis z until axis the until reading the reading of the of load the sensor load sensor reaches reaches target target value. value.After a After few secondsa few seconds containing containing a target a target load (within load (w 10ithin s),the 10 s), indenter the indenter rises up rises from upthe from surface the surface of the ofspecimen. the specimen. Then, theThen, optical the microscopeoptical microscope moves along move thes along x axis tothe replace x axis theto positionreplace the of indenter position and of indenterenables researchersand enables to researchers observe the to impression observe the caused impression by indenter caused through by indenter a charge through coupled a charge device coupled(CCD) camera. device (CCD) camera.

Figure 1. SchematicSchematic diagram diagram of of a a micro-hardness micro-hardness system. CCD—charge CCD—charge coupled device.

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Micro-hardness technique is highly inseparable from macro-hardness technique, where the only differenceMicro-hardness is the testing technique load range is highly applied inseparable by indenter. from In macro-hardness general, the tests technique, with indentation where the load only betweendifference 9.8 is × the 10 testing−3 N and load 1.961 range N are applied referred by to indenter. as micro-hardness In general, process, the tests while with indentationmacro-hardness load between 9.8 10 3 N and 1.961 N are referred to as micro-hardness process, while macro-hardness process is usually× − conducted over 49.03 N [28]. It can be easily found that the value of the indentation processload are is all usually integer conducted multipleover of gravitational 49.03 N [28]. acceleration It can be easily (~9.807 found m/s that2). theThis value is due of theto indentationa historical 2 precedentload are all that integer people multiple used standard of gravitational weights acceleration(like 1 kg and (~9.807 10 kg) m to/s apply). This the is indentation due to a historical load at precedentthe early stage that of people hardness used technique. standard weightsEven though (like 1the kg standard and 10 kg) weights to apply have the been indentation widely replaced load at bythe load early sensors stage of at hardness present, technique. people still Even adopt though the multiple the standard or semi-multiple weights have value been widelyof gravitational replaced accelerationby load sensors to conduct at present, micro-hardness people still tests. adopt the multiple or semi-multiple value of gravitational accelerationThe testing to conduct procedure micro-hardness of micro-hardness tests. testing is succinct and provides ideas for the subsequentThe testing nanoindentation procedure of micro-hardnesstesting technique. testing The is indenters succinct and used provides in micro-hardness ideas for the subsequenttesting are generallynanoindentation Vickers testing indenter technique. and Knoop The indentersindenter, usedwhile in the micro-hardness former is more testing common. are generally The tip Vickers of the Vickersindenter indenter and Knoop is a pyramid indenter, with while four the geometri former iscally more symmetric common. edges, The tip where of the the Vickers angle indenterbetween isthe a pyramidopposite withfaces four is 160°. geometrically Figure 2 gives symmetric the schema edges,tic where diagram the angle of residual between impression the opposite conducted faces is 160 by◦. VickersFigure2 indenter.gives the Under schematic ideal diagram conditions, of residual the shape impression of the impression conducted is bya square, Vickers and indenter. the lengths Under of diagonalideal conditions, (d1 and the d2) shape can be of thecalculated impression through is a square, the relative and the position lengths of of the diagonal vertexes (d1 observed and d2) canby opticalbe calculated microscope. through the relative position of the vertexes observed by optical microscope.

Figure 2. SchematicSchematic diagram of residual impression.

The Vickers hardness number, inin termsterms ofof NN andand m,m, isis calculatedcalculated asas followsfollows [[28]:28]: 𝑃 2𝑃sin (𝛼/2) 𝐻𝑉 =P = 2P sin(α/2) (1) HV = 𝐴 = 𝑑 (1) A d2 𝑃 𝐻𝑉 = 1.8544 × P (2) HV = 1.8544 𝑑 (2) × d2 where: where:P—indentation force, N; P—indentationA—area of force,the residual N; impression, m2; A—aread—mean of the diagonal residual impression,length of the m impression,2; m; and α—face angle of the Vickers indenter, 68°. d—mean diagonal length of the impression, m; and During the above calculation process, people assume that there is no recovery occurred when α—face angle of the Vickers indenter, 68◦. the indenter is removed after loading cycle. That is, it is assumed that the indentation retains the shapeDuring of the the indenter above calculation after the process,force ispeople remove assumed, which that thereis fundamentally is no recovery different occurred from when the nanoindentationindenter is removed introduced after loading in the cycle. next section. That is, On it is the assumed other hand, that the the indentation size of the residual retains the impression shape of canthe indenterbe extremely after small the force when is the removed, indentation which load is fundamentally is tiny. In general, different it is suitable from the to nanoindentationadopt an optical microscopeintroduced inmeasuring the next section. the leng Onth of the diagonals other hand, over the 20 size μm, of while the residual the observation impression of candiagonal be extremely length undersmall when10 μm theneeds indentation the assist loadof SEM. is tiny. However, In general, the greate it isst suitable strength to of adopt micro-hardness an optical technique microscope is themeasuring convenient the and length intuitive of diagonals testing overprocedure, 20 µm, while while the the observation observation under of diagonal SEM complicated length under the 10hardnessµm needs acquisition the assist process of SEM. through However, micro-hardne the greatestss. strengthThus, researchers of micro-hardness devoted techniqueto find a ismore the efficientconvenient method and intuitive to obtain testing the procedure, hardness while of thematerial observation under under tiny SEMindentation complicated load, the hardnessand the nanoindentationacquisition process was through developed micro-hardness. in succession. Thus, researchers devoted to find a more efficient method

2.2. Depth-Sensing Nanoindentation Testing

Micromachines 2020, 11, 407 4 of 25 to obtain the hardness of material under tiny indentation load, and the nanoindentation was developed in succession. Micromachines 2020, 11, x 4 of 25 Micromachines2.2. Depth-Sensing 2020, 11, Nanoindentationx Testing 4 of 25 2.2.1. Nanoindentation System 2.2.1. Nanoindentation Nanoindentation System Nanoindentation testing technique was essentially developed on the basis of micro-hardness Nanoindentation testing technique was essentially developed on the basis of micro-hardness technique, with attaching an additional displacement detecting sensor of indenter and converting the technique, with with attaching attaching an an additional additional displacement displacement detecting detecting sensor sensor of indenter of indenter and and converting converting the load sensor with smaller range, as called depth-sensing indentation (DSI) technique [29]. The loadthe loadsensor sensor withwith smaller smaller range, range, as called as called depth-sensing depth-sensing indentation indentation (DSI) (DSI)technique technique [29]. [The29]. nanoindentation systems can be mainly divided into two different types, based on driving principles: Thenanoindentation nanoindentation systems systems can be can mainly be mainlydivided divided into two into different two ditypes,fferent based types, on driving based onprinciples: driving electrostatic force and converse piezoelectric effect [30–32]. principles:electrostatic electrostatic force and converse force and piezoelectric converse piezoelectric effect [30–32]. effect [30–32]. The electrostatic driving method is based on the interaction between charged electrode plates, The electrostatic driving method is based on the interaction between charged electrode plates, plates, as shown in Figure 3, in which exertion of the load and monitor of the displacement can be realized as shown in Figure 33,, inin whichwhich exertionexertion ofof thethe loadload andand monitormonitor ofof thethe displacementdisplacement cancan bebe realizedrealized through one single component: three-plate capacitive transducer. The resolution and minimum through one singlesingle component:component: three-plate capacitivecapacitive transducer. The The resolution and minimum indentation load can be extremely tiny, adopting the electrostatic force driving method as 100 μN in indentation load can be be extremely extremely tiny, tiny, adopting the electrostatic force driving method as 100 μµN in theory, which becomes the basis of basically all the current investigations with maximum indentation theory, whichwhich becomesbecomes thethe basis of basically all the current current investigations investigations with maximum maximum indentation indentation load under 1 mN. load under 1 mN.

Figure 3. Schematic diagram of electrostatic driving method. Figure 3. SchematicSchematic diagram of electrostatic driving method. By contrast, the method driven by piezoelectric ceramic is more suitable for researchers tending By contrast, thethe methodmethod drivendriven byby piezoelectric piezoelectric ceramic ceramic is is more more suitable suitable for for researchers researchers tending tending to to build experimental platform by themselves, as shown in Figure 4. The recording data processes of tobuild build experimental experimental platform platform by themselves,by themselves, as shown as shown in Figure in Figure4. The 4. recordingThe recording data processesdata processes of load of load and displacement are separated through load sensor and capacitive displacement sensor, loadand displacementand displacement are separated are separated through through load sensor load and sensor capacitive and displacementcapacitive displacement sensor, respectively, sensor, respectively, leading to the reduction of the complexity of the assembly and the precise of the respectively,leading to the leading reduction to the of the reduction complexity of the of thecomplexity assembly of and the the assembly precise ofand the the involved precise units of the in involved units in contrast with electrostatic force method. Meanwhile, the maximum indentation involvedcontrast with units electrostatic in contrast force with method. electrostatic Meanwhile, force method. the maximum Meanwhile, indentation the maximum load can also indentation be raised load can also be raised largely to 1N (even 10 N), which has an overlapping range with micro- loadlargely can to also 1N (evenbe raised 10 N), largely which to has 1N an (even overlapping 10 N), rangewhich with has micro-hardnessan overlapping testing. range with micro- hardness testing. hardness testing.

Figure 4. Schematic diagram of piezoelectric driving method [[33].33]. Figure 4. Schematic diagram of piezoelectric driving method [33]. Besides the different driving principles, an integrated nanoindentation system usually contains Besides the different driving principles, an integrated nanoindentation system usually contains several essential components: several essential components: • Macroscopic motion unit: commonly actuated by electric motors to realize the millimeter scale • Macroscopic motion unit: commonly actuated by electric motors to realize the millimeter scale motion, including the rapid approaching of the indenter to the surface of specimen along z axis, motion, including the rapid approaching of the indenter to the surface of specimen along z axis, and the position change of the specimen in xy plane. Actually, this unit is quite similar to the and the position change of the specimen in xy plane. Actually, this unit is quite similar to the motion unit in micro-hardness testing system. motion unit in micro-hardness testing system.

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Besides the different driving principles, an integrated nanoindentation system usually contains several essential components: Macroscopic motion unit: commonly actuated by electric motors to realize the millimeter scale • motion, including the rapid approaching of the indenter to the surface of specimen along z axis, and the position change of the specimen in xy plane. Actually, this unit is quite similar to the motion unit in micro-hardness testing system. Loading unit: actuated by electrostatic capacity, magnetic coils, or piezoelectric stack to realize the • nanometer scale motion of indenter along the z axis, including the pre-touch process (right before the touch moment between indenter and specimen, while the reading of the load sensor is zero) and indentation process. Acquisition unit: mainly referring to load and displacement sensor, which are the most essential • parameters during nanoindentation experiment and subsequent data analysis process. The data of load and displacement should ideally be pertained to indenter and embodies the superiority combined with micro-hardness technique. Observation unit: a set of optical microscope is usually provided in commercial nanoindentation • system. Different from the dimension measurement of residual impression in micro-hardness testing, the microscope in nanoindentation technique is mainly used for determine indentation region of the specimen, as the size of the residual impression conducted by nanoindentation is so tiny. Control system: receiving and processing the signal from load and displacement sensors on • computer. Meanwhile, the loading unit is also controlled to adjust the loading rate in real time during the whole indentation procedure. The experimental results, including hardness and elastic modulus, are analyzed and calculated by control system after indentation testing. Indenter: realizing the impressing process during indentation process. • The indenter mainly involves Vickers indenter, Berkovich indenter (three pyramids), cube corner indenter, spheroconical indenter, and flat-ended indenter, corresponding to the different research purpose. However, the most widely used Vickers indenter in micro-hardness is currently substituted by Berkovich type in nanoindentation tests. The ineluctable line of junction occurred between opposite faces (Figure1c) during the manufacturing process in Vickers indenter seriously a ffected its application in tiny load tests.

2.2.2. Nanoindentation Theories The initial purpose of development of nanoindentation technique can be regarded as utilizing the data obtained by load and displacement sensors to calculate the mechanical properties, instead of direct measurement of the size of residual impressions in micro-hardness testing. Benefitting from the real time acquisition of load sensor and proportional-integral-derivative (PID) control of load unit through computer, nanoindentation testing can realize a load-control indentation process, as shown in Figure5a. The corresponding indentation curve ( P-h curve) is shown in Figure5b. In the past several decades, theories of nanoindentation have been developed to calculate mechanical properties basing on P-h curve. Oliver-Pharr model is the most representative and basis of most other analysis methods [7,29]. It is assumed that the loading part of indentation is an elastic-plastic contact process, while the unloading part is purely elastic. Thus, not only the hardness, but the elastic modulus of specimen can also be obtained through unloading curve. The relationship formulated between indentation load P and displacement h during the unloading process (CD section in Figure5b) is considered as a power law relation: P = α(h h )m (3) − f where hf is the depth of residual depth after indentation, and α and m are power law fitting constants related to specific unloading curve. The stiffness S, which is related to overall elastic recovery of during the unloading process, can be calculated by the slope at the vertex of the unloading curve: Micromachines 2020, 11, 407 6 of 25 Micromachines 2020, 11, x 5 of 25

• Loading unit: actuated by electrostatic capacity,dP magnetic coils, or piezoelectric stack to realize the nanometer scale motion of indenterS = along the z axis, including the pre-touch process (right (4) dh = before the touch moment between indenter andh specimen,hmax while the reading of the load sensor is zero) and indentation process. For calculation of hardness H, the true indentation depth hc (the vertical distance between the tip • Acquisition unit: mainly referring to load and displacement sensor, which are the most essential of indenter and the point where indenter and surface of specimen separated at maximum indentation parameters during nanoindentation experiment and subsequent data analysis process. The data depth) is calculated as: of load and displacement should ideally be pertained to indenter and embodies the superiority Pmax combined with micro-hardnesshc = technique.hmax h s = hmax ε (5) − − S • Observation unit: a set of optical microscope is usually provided in commercial nanoindentation where hs issystem. the elastic Different deformation from the dimension around indentationmeasurement region of residual and willimpression recover in tomicro-hardness flat surface after unloading,testing, and εtheis microscope a constant in only nanoindentation relation with technique the shape is mainly of indenter. used for Then,determine the indentation hardness H of specimenregion can be of calculated the specimen, as: as the size of the residual impression conducted by nanoindentation is so tiny. Pmax H = (6) • Control system: receiving and processing the Asignal from load and displacement sensors on where A iscomputer. the true projectedMeanwhile, contact the loading area betweenunit is also indenter controlled and to surface,adjust the and loading it can rate be calculatedin real time from during the whole indentation procedure. The experimental results, including hardness and hc and geometry of indenter. The relationship between A and hc of ideal indenter is: elastic modulus, are analyzed and calculated by control system after indentation testing. • Indenter: realizing the impressing process during2 indentation process. A = ξhc (7) The indenter mainly involves Vickers indenter, Berkovich indenter (three pyramids), cube wherecornerξ is a indenter, constant spheroconical only relation indenter, with the shapeand flat of-ended indenter indenter, (Berkovich, correspondingξ = 24.56). to the different Forresearch calculation purpose. of However, elastic modulus the mostE ,widely the reduced used Vickers modulus indenterEr (combined in micro-hardness modulus is of currently the indenter and specimen)substituted can by beBerkovich determined type in as: nanoindentation tests. The ineluctable line of junction occurred between opposite faces (Figure 1c) during the manu√π facturingS process in Vickers indenter seriously affected its application in tiny load tests. Er = (8) 2β √A where2.2.2.β is Nanoindentation a constant related Theories with the shape of indenter. The elastic modulus of specimen can be given as: The initial purpose of development of nanoindentation technique can be regarded as utilizing 2 the data obtained by load and displacement1 1sensorν s to1 calculateν2 the mechanical properties, instead = − i + − (9) of direct measurement of the size of residualEr imprEi essions Ein micro-hardness testing. Benefitting from the real time acquisition of load sensor and proportional-integral-derivative (PID) control of load unit where ν is the Poisson’s ratio of specimen, and νi and Ei are the Poisson’s ratio and elastic modulus of through computer, nanoindentation testing can realize a load-control indentation process, as shown indenter, respectively. in Figure 5a. The corresponding indentation curve (P-h curve) is shown in Figure 5b.

FigureFigure 5. Schematic 5. Schematic diagram diagram ofof nanoindentation. (a) Typical (a) Typical load-time load-time (P-t) curve. (P-t) ( curve.b) Typical (b load-) Typical load-displacementdisplacement (P-h (P-h) curve.) curve. (c) (Physicalc) Physical meaning meaning of parameters of parameters in calculation in calculation process. process.

Through Oliver-Pharr method, researchers can effectively obtain mechanical properties of material without directly observing the residual impression under microscope. However, the calculation of the hardness and elastic modulus is indirect and involves calculated parameters. For instance, the Micromachines 2020, 11, 407 7 of 25 obtaining process of hardness essentially relies on the estimation of residual contact area, which follows the calculation method of micro-hardness testing. The determination of hs and A can be intensely influenced by specific phenomenon during the indentation process, e. g., pile-up and creep. Thus, several correction methods have been proposed to improve Oliver-Pharr method to adapt different application scenarios [34–36]. The same situation also occurs in low temperature nanoindentation testing, which will be discussed in following, Section4.

3. Technical Development of Low Temperature Nanoindentation System A low temperature environment is relative to the ambient temperature (room temperature (RT) 293 K), generally referring to the temperature range between RT and absolute zero (0 K). It has several call methods for the division of temperature value: cold, low, cryogenic (referring in particular to temperature below 120 K), and ultra-low temperature, while researchers choose the specific name according to their investigation temperature range [37–39]. In this article, “low temperature” is employed to describe temperatures below RT universally in order to simplify the writing. Generally, the core of the realization of a low temperature environment is cryogenic technology, such as liquid vaporization refrigeration, thermoelectric refrigeration, and magnetic refrigeration [40–42]. Low temperature state can be applied on the subject and/or atmosphere which researchers hope to refrigerate. In the field of material testing, a low temperature environment is most frequently exerted on the uniaxial tensile tests, which is conducive to understand strength, elasticity, and plasticity macroscopically [43–45]. Correspondingly, indentation technology attached with a low temperature environment provides the possibility to investigate micro and nano mechanical properties of materials. The current developed low temperature indentation apparatuses can be generally divided into two types according to the principle of refrigeration: system immersed in cryogenic liquid and contact-type low temperature testing.

3.1. System Immersed in Cryogenic Liquid The very earliest indentation testing combined with a low temperature environment can be traced back to the 1960s. Marsh et al. attempted to utilize liquid nitrogen (LN2) to cool down and obtain a low temperature specimen [46], as shown in Figure6a. An uncovered vessel was used to contain LN 2 and specimen, while the specimen was fully immersed into the liquid. As the boiling point of the LN2 is 76.59 K (~77 K) under atmospheric pressure, the temperature of the specimen immersed in LN2 is generally considered as constant 77 K. To conduct the indentation process, a normal Vickers hardness tester was firstly employed. Limited by the space of the Vickers indenter, researchers had to wait for the LN2 naturally evaporating until leaving only a thin layer over the specimen surface, and then raise theMicromachines vessel and 2020 specimen, 11, x rapidly to the Vickers indenter to conduct indentation. 8 of 25

Figure 6. Schematic diagram of indentation test immersed in liquid nitrogen (LN(LN22). ( (aa)) Original Original setup. setup. ((bb)) ImprovedImproved setup.setup.

An apparatus with lower indentation temperature was developed in Niigata University in 1996, which realized hardness testing at 4.2 K [47]. Figure 7a only shows schematic diagram of the cryogenic assembly and indentation region of the apparatus, as the overall height is ~2 m. The unexpressed parts are related mechanical devices, which drive the indenter vertically approaching and applying the load, as well as the specimen rotating in the horizontal plane to change the indentation area, respectively. The specimen and indenter were immersed in liquid helium (LHe, with a boiling point of 4.2 K) in a cryostat. To reduce the consumption of LHe, an extra cryostat filled with LN2 was placed outside the 1st cryostat as a cold shield. The specimen was fixed on the bottom of a cylinder pipe, while the indenter and load sensor were placed at the end of a loading shaft, which is supported by a polyimide sleeve inserted in a support pipe. Though friction was inevitable between the shaft and sleeve, the load sensor was separate beneath the friction area and unaffected from the friction. Additionally, the test temperature was actually controlled by liquid type, resulting in three available temperatures (4.2 K, 77 K, and RT).

Figure 7. (a) Schematic diagram of 4.2 K indentation device. (b) Realization of temperature variation of specimen [47]. LHe = liquid helium.

To obtain continuous temperature variation with the apparatus in Figure 7a, researchers adopted natural evaporation method of LHe inside cryostat before indentation [48]. With the LHe level went down below specimen, the temperature of specimen rose gradually due to the heat condition from the outside. Figure 7b shows the temperature rise of the specimen with time. It can be noticed that there was a temperature rapidly rising stage after LHe evaporating completely, where the maximum rising rate was 2.67 K/min. This is not conducive to conducting repeated experiments

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MicromachinesHowever, 2020 a, 11 considerable, x flaw of such a method was found that a great deal of heat flowed8 of 25 from the RT diamond indenter to the specimen, inducing that the indentation area was warmed up during contact. To eliminate the temperature diffusion problem, researchers expanded the distance between specimen and liquid surface, while the Vickers indenter was immersed into the LN2 before the indentation process. The connection between the indenter and the hardness testing machine was Tufnol rod, which effectively prevented heat flowing to indenter from upper upsets. Kurkjian et al. improved the LN2 immersed method by substituting polystyrene dewar (with a lid) and phenol fiber rod for common uncovered vessel and Tufnol rod, respectively [24], as shown in Figure6b. Meanwhile, a chromel-alumel thermocouple was attached to the indenter with a small area to monitor testing temperature. To a certain extent, these improvements increased the accuracy of indentation tests. However, the additive thermocouple only played a role of monitoring, but not controlling the temperature. The utilization of LN2 limited the testing on a specific temperature point, and research has showed that the sudden low temperature applied on the specimen usually caused cracks. More importantly, the temperature control of LN2 is relied on the boiling point, leading to a constant boiling phenomenon. The produced nitrogen bubbles resulted in turbulence inside the dewar Figure 6. Schematic diagram of indentation test immersed in liquid nitrogen (LN2). (a) Original setup. and partial bubbles directly stroked the indenter, which affected the measurement of load during the (b) Improved setup. indentation process. An apparatus with lower indentation temperature was developed in Niigata University in 1996, An apparatus with lower indentation temperature was developed in Niigata University in 1996, which realized hardness testing at 4.2 K [47]. Figure7a only shows schematic diagram of the cryogenic which realized hardness testing at 4.2 K [47]. Figure 7a only shows schematic diagram of the assembly and indentation region of the apparatus, as the overall height is ~2 m. The unexpressed parts cryogenic assembly and indentation region of the apparatus, as the overall height is ~2 m. The are related mechanical devices, which drive the indenter vertically approaching and applying the load, unexpressed parts are related mechanical devices, which drive the indenter vertically approaching as well as the specimen rotating in the horizontal plane to change the indentation area, respectively. and applying the load, as well as the specimen rotating in the horizontal plane to change the Theindentation specimen area, and respectively. indenter were Th immersede specimen in and liquid indenter helium were (LHe, immersed with a boiling in liquid point helium of 4.2 (LHe, K) in awith cryostat. a boiling To reducepoint of the 4.2 consumption K) in a cryostat. of LHe, To reduce an extra the cryostatconsumption filled of with LHe, LN an2 was extra placed cryostat outside filled the 1st cryostat as a cold shield. The specimen was fixed on the bottom of a cylinder pipe, while the with LN2 was placed outside the 1st cryostat as a cold shield. The specimen was fixed on the bottom indenterof a cylinder and loadpipe, sensor while the were indenter placed atand the load end sensor of a loading were placed shaft, whichat the end is supported of a loading by ashaft, polyimide which sleeveis supported inserted by in a apolyimide support pipe. sleeve Though inserted friction in a support was inevitable pipe. Though between friction the shaft was and inevitable sleeve, between the load sensorthe shaft was and separate sleeve, beneath the load the sensor friction was area separate and una beneathffected the from friction the friction. area and Additionally, unaffected from the test the temperaturefriction. Additionally, was actually the controlledtest temperature by liquid was type, actually resulting controlled in three by available liquid type, temperatures resulting in (4.2 three K, 77available K, and RT).temperatures (4.2 K, 77 K, and RT).

FigureFigure 7.7. ((aa)) SchematicSchematic diagramdiagram ofof 4.24.2 KK indentationindentation device.device. ((bb)) RealizationRealization ofof temperaturetemperature variationvariation ofof specimenspecimen [[47].47]. LHeLHe == liquid helium.

To obtain continuous temperature variation with the apparatus in Figure7a, researchers adopted To obtain continuous temperature variation with the apparatus in Figure 7a, researchers natural evaporation method of LHe inside cryostat before indentation [48]. With the LHe level went adopted natural evaporation method of LHe inside cryostat before indentation [48]. With the LHe down below specimen, the temperature of specimen rose gradually due to the heat condition from the level went down below specimen, the temperature of specimen rose gradually due to the heat condition from the outside. Figure 7b shows the temperature rise of the specimen with time. It can be noticed that there was a temperature rapidly rising stage after LHe evaporating completely, where the maximum rising rate was 2.67 K/min. This is not conducive to conducting repeated experiments

Micromachines 2020, 11, 407 9 of 25 outside. Figure7b shows the temperature rise of the specimen with time. It can be noticed that there was a temperature rapidly rising stage after LHe evaporating completely, where the maximum rising Micromachines 2020, 11, x 9 of 25 rate was 2.67 K/min. This is not conducive to conducting repeated experiments at specific temperature, atand specific the indentation temperature, process and should the indentation be carefully process controlled should to avoid be carefully the experimental controlled error to inducedavoid the by experimentaltemperature variation.error induced Similarly, by temperature another temperature variation. Similarly, rapidly rising another stage temperature with larger rapidly temperature rising stagespan with also occurredlarger temperature between 100 span K also and occurred 293 K, which between was 100 not K mentioned and 293 K, inwhich the research.was not mentioned Thus, the inuncontrolled the research. temperature Thus, the risinguncontrolled rate limited temperature the usability rising of rate hardness limited testing the usability under continuouslyof hardness testingvariable under temperature. continuously variable temperature. InIn general, general, the the low low temperature temperature indentation indentation method method realized realized with with system system immersed immersed in in cryogenic cryogenic liquidliquid is advantageous to realization hardness testingtesting atat specificspecific temperature.temperature. The The apparatus apparatus is is considerably simple and the essential assembly only contains cryogenic liqu liquid,id, insulated vessel, and a conventional indentation setup. However, However, the the natural natural boiling boiling point point limits limits the the application of the method on variable temperatures. More More importantly, importantly, the tests conducted by the system immersed in cryogenic liquidliquid werewere limited limited to to hardness hardness testing, testing, which which lacked lacked the measurementthe measurement of indentation of indentation depth, depth,inducing inducing the absence the absence of more of mechanical more mechanical properties properties obtaining obtaining from P-h fromcurves. P-h curves. 3.2. Contact-Type Low Temperature Testing 3.2. Contact-Type Low Temperature Testing To avoid the shortcomings of directly immersion method, researchers tried to adopt indirect To avoid the shortcomings of directly immersion method, researchers tried to adopt indirect methods to realize indentation at controllable low temperatures. Researchers from Iwate University methods to realize indentation at controllable low temperatures. Researchers from Iwate University improved the apparatus in Figure7a with the ability of conducting indentation at continuously improved the apparatus in Figure 7a with the ability of conducting indentation at continuously variable temperatures [49], as shown in Figure8. The same mechanical loading setup was adopted variable temperatures [49], as shown in Figure 8. The same mechanical loading setup was adopted in in the apparatus except for an additional differential transformer parallel to the loading shaft, which the apparatus except for an additional differential transformer parallel to the loading shaft, which deformed with the motion and measured the displacement of the indenter. The specimen was fixed on deformed with the motion and measured the displacement of the indenter. The specimen was fixed the specimen holder (with heaters inside) which was connected to the 2nd stage of a Gifford-McMahon on the specimen holder (with heaters inside) which was connected to the 2nd stage of a Gifford- (GM) refrigerator. A thermocouple was glued on the side of the specimen with Ag paste bond grease McMahon (GM) refrigerator. A thermocouple was glued on the side of the specimen with Ag paste to control the testing temperature via GM refrigerator and heaters. The lowest cooling temperature can bond grease to control the testing temperature via GM refrigerator and heaters. The lowest cooling reach 40 K, and the accuracy of temperature controlling was within 1 K. Meanwhile, an additional temperature can reach 40 K, and the accuracy of temperature controlling± was within ±1 K. Meanwhile, thermocouple was placed onside the indenter, which only played a role in monitoring the temperature an additional thermocouple was placed onside the indenter, which only played a role in monitoring variation of indenter. For this reason, a problem of heat flow from indenter similar with apparatus in the temperature variation of indenter. For this reason, a problem of heat flow from indenter similar Figure6a occurred, influencing the temperature around indentation area. with apparatus in Figure 6a occurred, influencing the temperature around indentation area.

FigureFigure 8. 8. SchematicSchematic diagram diagram of of indentation indentation apparatus apparatus with with Gifford-McMahon Gifford-McMahon (GM) refrigerator.

The driving mode of the indentation apparatuses introduced above were all based on electric motor (improved from hardness tester), inducing that the indentation load was limited at newton level.level. With With the the development development of of a a modern modern DSI DSI appara apparatustus during during recent recent two two decades, decades, the the resolution resolution of of displacement and load of low temperature indentation were increased accordingly. Pethica et al. combined combined electrostatic electrostatic driving driving method method (Figure (Figure 33)) withwith PeltierPeltier coolers,coolers, realizingrealizing nanoindentation atat low low temperatures temperatures [50 [50],], as shownas show inn Figure in Figure9 (driving 9 (driving setups notsetups shown). not shown). The indenter The indenter and the specimen were, respectively, fixed on two separated Peltier coolers through copper plates. As the working of the Peltier coolers were based on thermoelectric effect, heat sinks were placed behind the Peltier coolers to cool down the high temperature side. The temperature of the specimen and indenter can be simply controlled via adjusting the supplied DC voltage of the Peltier

Micromachines 2020, 11, 407 10 of 25 and the specimen were, respectively, fixed on two separated Peltier coolers through copper plates. As the working of the Peltier coolers were based on thermoelectric effect, heat sinks were placed behind the Peltier coolers to cool down the high temperature side. The temperature of the specimen Micromachines 2020, 11, x 10 of 25 and indenter can be simply controlled via adjusting the supplied DC voltage of the Peltier coolers. coolers.The mass The of mass the Peltier of the set Peltier besides set besides the indenter the indent was lightweighter was lightweight enough enough to avoiding to avoiding the effect the during effect duringthe indentation the indentation process. process.

FigureFigure 9. 9. SchematicSchematic diagram diagram of of depth-sensing depth-sensing indentat indentationion (DSI) (DSI) apparatus apparatus with with Peltier Peltier cooler. cooler.

However, the the apparatus apparatus in in Figure Figure 9 9was was open, open, and and ice iceoccurred occurred during during the cooling the cooling process process when thewhen temperature the temperature fell below fell 0 below °C. Chenc 0 ◦C. et Chenc al. improv et al.ed improved the apparatus the apparatus [51] with: [(1)51] setting with: (1)the settingwhole apparatusthe whole into apparatus a sealed into chamber a sealed purging chamber with purging argon gas with inside argon to prevent gas inside water to preventvapor condensation; water vapor andcondensation; (2) substituting and (2)the substitutingheat sink with the water heat cooler sink with to achieve water coolerbetter cooling to achieve effect. better The coolingadvantage effect. of adoptingThe advantage Peltier of coolers adopting was Peltier convenient coolers and was low convenient cost, while and lowthe cost,temperature while the of temperature the indenter of and the specimenindenter and could specimen be controlled could beindependently controlled independently to be identical. to However, be identical. the However,cooling power the cooling of miniature power Peltierof miniature coolers Peltier limited coolers the testing limited temperature the testing temperatureabove 220 K, above which 220 was K, the which highest was among the highest the several among methods.the several methods. To obtain obtain a alarger larger temperature temperature range range at the at thecond conditionition of continuous of continuous temperature temperature variation, variation, Zhao etZhao al. adopted et al. adopted commercial commercial cold coldfinger finger to realize to realize the the application application of ofa alow low temperature temperature environment environment down to 150 K [[33],33], as shown in Figure 1010a.a. The The whole mechanical setups setups were were set set in a vacuum chamber toto prevent prevent the the water water vapor vapor condensation. condensation The. occurrenceThe occurrence of icecould of ice be could effectively be effectively prevented 2 −2 preventedat vacuum at degree vacuum below degree 10− belowPa. Lee 10 et Pa. al. adoptedLee et al. a adopted scanning a electronscanning microscope electron microscope (SEM), providing (SEM), providinga vacuum a environment vacuum environment and realized and in-situ realized indentation in-situ indentation observation observation ulteriorly ulteriorly [52]. The [52]. working The workingprinciple principle of the cold of finger the cold is shown finger in is Figure shown 10b. in Nitrogen Figure 10b. with Nitrogen controlled with pressure controlled stimulated pressure LN2 stimulatedin dewar to LN flow2 in intodewar a vacuumto flow into jacketed a vacuum transfer jacketed line, transfer which insulated line, which heat insulated exchange heat of exchange LN2 and ofcarried LN2 and LN 2carriedinto the LN flow2 into path the of flow the coldpath finger.of the cold The flowfinger. controllable The flow controllable LN2 absorbed LN the2 absorbed heat of cold the heatfinger of andcold was finger excreted and was outside excreted the vacuumoutside the chamber vacuum in nitrogenchamber state. in nitrogen state. An electric heater and silicon diode were set inside the end of the cold finger to realize PID control of the temperature within 0.05 K. However, the setup of cold finger was too cumbersome to be ± contacted with the indenter directly. Researchers bonded the end of the cold finger and indenter with a section of copper wire to cool down the indenter to a certain extent. For this reason, the temperature of indenter could not be adjusted finely, and the difference between indenter and specimen was inevitable. Other means should be taken to avoid the related effect, which will be introduced in the next section.

Figure 10. Schematic diagram of DSI apparatus with cold finger (a) indentation setups inside vacuum chamber (b) cooling system [33].

An electric heater and silicon diode were set inside the end of the cold finger to realize PID control of the temperature within ± 0.05 K. However, the setup of cold finger was too cumbersome to be contacted with the indenter directly. Researchers bonded the end of the cold finger and indenter

Micromachines 2020, 11, x 10 of 25 coolers. The mass of the Peltier set besides the indenter was lightweight enough to avoiding the effect during the indentation process.

Figure 9. Schematic diagram of depth-sensing indentation (DSI) apparatus with Peltier cooler.

However, the apparatus in Figure 9 was open, and ice occurred during the cooling process when the temperature fell below 0 °C. Chenc et al. improved the apparatus [51] with: (1) setting the whole apparatus into a sealed chamber purging with argon gas inside to prevent water vapor condensation; and (2) substituting the heat sink with water cooler to achieve better cooling effect. The advantage of adopting Peltier coolers was convenient and low cost, while the temperature of the indenter and specimen could be controlled independently to be identical. However, the cooling power of miniature Peltier coolers limited the testing temperature above 220 K, which was the highest among the several methods. To obtain a larger temperature range at the condition of continuous temperature variation, Zhao et al. adopted commercial cold finger to realize the application of a low temperature environment down to 150 K [33], as shown in Figure 10a. The whole mechanical setups were set in a vacuum chamber to prevent the water vapor condensation. The occurrence of ice could be effectively prevented at vacuum degree below 10−2 Pa. Lee et al. adopted a scanning electron microscope (SEM), providing a vacuum environment and realized in-situ indentation observation ulteriorly [52]. The working principle of the cold finger is shown in Figure 10b. Nitrogen with controlled pressure stimulated LN2 in dewar to flow into a vacuum jacketed transfer line, which insulated heat exchange ofMicromachines LN2 and carried2020, 11, 407LN2 into the flow path of the cold finger. The flow controllable LN2 absorbed11 ofthe 25 heat of cold finger and was excreted outside the vacuum chamber in nitrogen state.

FigureFigure 10. 10. SchematicSchematic diagram diagram of of DSI DSI apparatus apparatus with with cold cold finger finger ( (aa)) indentation indentation setups setups inside inside vacuum vacuum chamberchamber ( (bb)) cooling cooling system system [33]. [33]. 4. Influence Factors and Management An electric heater and silicon diode were set inside the end of the cold finger to realize PID controlThe of developmentthe temperature of within nanoindentation ± 0.05 K. However, technology the setup was basedof cold onfinger the was high too accuracy cumbersome of data to beacquisition, contacted especiallywith the indenter the indentation directly.P-h Researchercurves. Fors bonded this purpose, the end certain of the kindscold finger of works, and includingindenter calibration of sensors, correction of flexibility of apparatus, and area function of indenter, should be conducted before the indentation process [53–55]. Meanwhile, a series of calculation was conducted based on P-h curves to obtain mechanical properties, as introduced in Section2. However, the additional low temperature environment usually affected the accuracy of acquisition and processing of nanoindentation data. The influence factors mainly reflected on three aspects: thermal drift, variation from indenter, and variation from specimen.

4.1. Thermal Drift In nanoindentation testing, the measurement of true indentation displacement h is always difficult when comparing with load data. Under normal working circumstances, the determination of displacement only relies on indirect measurement of the displacement of one certain component in the apparatus (center plate and baffle in Figures3 and4, respectively) but not the direct movement of the tip of indenter. Thus, the transference of the displacement from indenter tip to the certain component can be easily affected by an external environment, especially temperature influence, which is defined as thermal drift. Thermal drift is induced from thermal expansion occurring somewhere within the apparatus and accumulated with time. Generally, thermal drift can be split into two separate contributions: frame drift and contact drift. Frame drift occurs due to temperature variations in the nanoindentation system frame away from the indentation contact area [56]. At room temperature, the frame drift can be effectively reduced through adopting a sealed cabinet outside the apparatus. At low temperatures, frame drift occurs due to thermal gradient of the active and passive cooling components and gradually decreasing temperature of sensors. The former generally decreases over time until stable thermal gradient of each components is established. The latter requires effective isolation between cooling components and sensors, which works within operating temperature range. In both cases, frame drift decreases over time until elimination. Nanoindentation tests should be conducted primarily at the condition of zero-drift status. However, as frame drift is independent of indentation area and information of materials, short period nanoindentation tests are considerable if the frame drift rate performs linear as a function of time. Contact drift occurs due to thermal deformation of the indenter during the nanoindentation process. Heat flow occurs between indenter and specimen at the contact area, induced by different temperatures between them [57,58]. At RT, the temperatures of indenter and specimen are same; thus, contact drift is negligible. In low temperature nanoindentation, if the indenter is not cooled or the Micromachines 2020, 11, 407 12 of 25

cooling effect is inadequate, the occurrence of contact drift will perform during contact, as shown in Figure 11. With the contact, heat flows from the indenter with higher temperature to the specimen, inducing the length of indenter decreased with temperature reducing. In order to keep the load constant in the moment, the indenter has to be driven downward to keep the contact area. Thus, the nanoindentationMicromachines 2020, 11P-h, x curves obtained with contact drift in load control mode will performed as shown12 of 25 in Figure 12a. Micromachines 2020, 11, x 12 of 25

Figure 11. Occurrence of contact drift during low temperature nanoindentation. RT—room temperature. FigureFigure 11.11. OccurrenceOccurrence of contactof contact drift duringdrift during low temperature low temperature nanoindentation. nanoindentation. RT—room temperature.RT—room temperature.

Figure 12. Indentation curves with contactcontact drift.drift. (a) P-h curve at RT and low temperature. (b)) h-t curve and P-t curvecurve withwith contactcontact drift.drift. Figure 12. Indentation curves with contact drift. (a) P-h curve at RT and low temperature. (b) h-t curve and P-t curve with contact drift. Figure 1212aa shows shows indentation indentation curves curves on copper on copper at 150 Kat with 150 andK with without and contact without drift, contact respectively. drift, The distance between the two curves under a certain load expresses the value of contact drift, which respectively.Figure 12a The shows distance indentation between the curves two curveson copper under at a certain150 K loadwith expresses and without the value contact of contact drift, isdrift, accumulated which is accumulated over time. Every over point time. in Every the P-h pointcurve in withthe P-h contact curve drift with becomes contact unreliable, drift becomes and respectively.even negative The sti distanceffness occurs between during thethe two unloading curves un process,der a certain which load is impossibleexpresses the for value copper of material.contact drift,unreliable, which andis accumulated even negative over stif fnesstime. occurs Every during point inthe the unloading P-h curve process, with whichcontact is drift impossible becomes for Tocopper measure material. the rate To of measure contactdrift, the rate researchers of contact generally drift, conductresearchers periods generally of holding conduct time duringperiods the of unreliable,indentation and process, even negative as shown stif infness Figure occurs 12b, withduring calculation the unloading formula: process, which is impossible for copperholding material. time during To measurethe indentation the rate process, of contact as shown drift, in researchers Figure 12b, generallywith calculation conduct formula: periods of holding time during the indentation process, as shown∆∆ℎh in Figure 12b, with calculation formula: D𝐷== (10)(10) ∆ℎt𝑡 𝐷= (10) wherewhere DD isis thermalthermal driftdrift rate,rate, andand ∆Δhh isis incrementincrement𝑡 ofof indentationindentation depthdepth detecteddetected byby displacementdisplacement wheresensorsensor D duringduring is thermal holding holding drift time timerate, t. The t.and The value Δ hvalue is of incrementD ofin lowD in temperature oflow indentation temperature nanoindentation depth nanoindentation detected is generallyby displacement is generally positive, sensorwhilepositive, itduring is while negative holding it is innegative high time temperature int. highThe valuetemperature nanoindentation. of D in nanoindentation. low temperature nanoindentation is generally positive,The while amountamount it is of negative heatheat flowflow in throughhighthrough temperature thethe contactcontact nanoindentation. dependsdepends on thethe realreal timetime contactcontact area,area, andand initialinitial temperaturetemperatureThe amount didifferencefference of heat between flowbetween through indenter indenter the and contact and specimen, spec dependsimen, which whichon are the impossible realare impossibletime tocontact be determined to area, be determinedand through initial temperatureexperimentalthrough experimental difference method. method. Itbetween is also inappropriateIt indenter is also inappropri and to spec adoptimen,ate laterto adoptwhich correction laterare impossiblecorrection after indentation afterto be indentation determined to eliminate to throughtheeliminate contact experimental the drift. contact Additionally, method.drift. Additionally, theIt is heat also flow inappropri the also heat causesate flow to temperature adoptalso causeslater variationcorrection temperature of after the variation specimenindentation of in theto eliminatecontactspecimen area, the in the whichcontact contact aff drift.ect area, the Additionally, actualwhich testingaffect thethe temperatures. actuheatal flowtesting also Thus, temperatures. causes researchers temperature Thus, adopted researchers variation several methodsadopted of the specimentoseveral reduce methods in the the temperature contact to reduce area, di ffwhichtheerence temperature affect for eliminating the actu differal testing theence contact for temperatures. eliminating drift through Thus, the physicalcontact researchers means.drift adopted through severalphysical methods means. to reduce the temperature difference for eliminating the contact drift through physicalIn themeans. immersed cooling method (Figure 6,7), the indentation region was set inside the same media.In the The immersed temperatures cooling of the method indenter (Figure and specimen 6,7), the indentationare absolutely region the same, was set and inside no contact the same drift media.needs toThe be temperatures eliminated. of the indenter and specimen are absolutely the same, and no contact drift needsIn to thebe eliminated.Peltier cooling method (Figure 9), two separated Peltier coolers were adopted to cool downIn thethe indenterPeltier cooling and specimen. method (FigureEven though 9), two the se cparatedooling effect Peltier of coolersPeltier werecooler adopted was affected to cool by downheat dissipation,the indenter which and specimen. is generally Even weakened though ovtheer c time,ooling the effect temperatures of Peltier coolerof the wastwo componentsaffected by heatcould dissipation, be well adjusted which combiningis generally with weakened thermal ov coupleser time, and the DC temperatures voltage under of PIDthe twocontrol. components Thus, the couldPeltier be cooling well adjusted method combining has the dominant with thermal advantage couples in andthe aspectDC voltage of contact under drift PID controlling. control. Thus, the

Peltier cooling method has the dominant advantage in the aspect of contact drift controlling.

Micromachines 2020, 11, 407 13 of 25

In the immersed cooling method (Figures6 and7), the indentation region was set inside the same media. The temperatures of the indenter and specimen are absolutely the same, and no contact drift needs to be eliminated. In the Peltier cooling method (Figure9), two separated Peltier coolers were adopted to cool down the indenter and specimen. Even though the cooling effect of Peltier cooler was affected by heat dissipation, which is generally weakened over time, the temperatures of the two components could be well adjusted combining with thermal couples and DC voltage under PID control. Thus, the Peltier cooling method has the dominant advantage in the aspect of contact drift controlling. In the cold finger cooling method (Figure 10), the specimen was exclusively cooled. Thus, the contact drift was larger than the other two methods. The cooling copper wire connecting the indenter and cold finger could only reduce the temperature difference to a certain extent, as shown in Table1[ 33]. To eliminate the contact drift, researchers kept the indenter in touched with the specimen for a period of time at a certain load, which is much higher than subsequent indentation load (generally more than 30 min). The touching time was generally extended with decreasing temperature. Combined with copper wire and pre-touched method, the thermal drift could be basically eliminated. However, the operation of the two methods was complex so that the shape of the copper should be carefully adjusted to avoid influence on the indentation process, and the cooling effect of pre-touched was not permanent, inducing multiple times of the pre-touch operation even under one certain testing temperature.

Table 1. Thermal drift rate under different cooling methods (nm/s) [33].

Temperature Original Copper Wire Pre-Touched 298 K 0.049 0.005 0.019 0.008 0.033 0.007 ± − ± ± 250 K 1.946 0.104 0.383 0.159 0.028 0.005 ± ± ± 200 K 3.793 0.344 0.774 0.208 0.063 0.008 ± ± ± 150 K 4.985 0.325 1.137 0.222 0.092 0.021 ± ± ±

4.2. Temperature Influence on Indenter Generally, researchers focused on the elimination of thermal drift in temperature nanoindentation to obtain accurate P-h curves and considered the indenter as constant. However, in well-controlled low temperature nanoindentation testing, both the specimen and indenter were in cold condition. The property variation of indenter also had influence on the experimental results, which should be fully considered.

4.2.1. Indentation Hardness The sapphire indenter had lower heat conductivity compared with diamond indenter and performed better in reducing thermal drift. However, as the sapphire indenter was a single crystalline with hexagonal system, the difference of thermal expansion rate between parallel and perpendicular directions to the c axis could induce shape variation at non-ambient temperatures, as shown in Figure 13a. For an equivalent conical indenter, the thermal expansion rate at perpendicular direction to the c axis is considered uniform. At non-ambient temperatures, the contact radius r deduced from indentation depth can be calculated as: γ r = k r (11) γ 0 ⊥ where γ and γ are the linear expansions at parallel and perpendicular directions to the c axis, k ⊥ respectively, and r0 is contact radius. Under the circumstance that assume the properties of testing material independent with temperature, the error of hardness ξH can be calculated as follows:

γ2 ξH = k 1. (12) γ2 − ⊥ Micromachines 2020, 11, 407 14 of 25

The calculated percentage error of hardness induced by thermal expansion anisotropy is presented in Figure 13b [33]. At low temperatures, the maximum error is ~ 0.02%, which is basically negligible to affect the hardness test. However, the calculated hardness is lower than the true value with temperature continued increasing, due to the decrease of equivalent half cone angle. Thus, the area function of the indenter at non-ambient temperatures requires careful consideration to calibrate the hardnessMicromachines calculation. 2020, 11, x 14 of 25

FigureFigure 13.13. ((a)) ThermalThermal deformationdeformation ofof sapphiresapphire indenterindenter atat lowlow temperatures.temperatures. ((b)) PercentagePercentage errorerror ofof hardnesshardness atat didifferentfferent temperaturestemperatures [33[33].].

The occurrence of nanoindentation hardness testing error proceeds from inaccurate estimation The occurrence of nanoindentation hardness testing error proceeds from inaccurate estimation of area function of indenter, inducing the P-h curves deviate from the accurate value. However, this of area function of indenter, inducing the P-h curves deviate from the accurate value. However, this error only occurs in DSI testing. In the situation of micro-hardness testing, the contact area is directly error only occurs in DSI testing. In the situation of micro-hardness testing, the contact area is directly measured after the whole indentation process, which is less depending on the shape of the indenter. measured after the whole indentation process, which is less depending on the shape of the indenter. However, in most hardness testing the determination process of residual impression area is conducted However, in most hardness testing the determination process of residual impression area is atconducted RT. The temperatureat RT. The temperature rising process rising will inevitablyprocess will lead inevitably to thermal lead deformation to thermal of deformation specimen and of residualspecimen impression, and residual while impression, the coeffi cientwhile of the thermal coefficient expansion of thermal is various expansion due to diis ffvariouserent material. due to Thus,different from material. this point Thus, of view, from thethis DSIpoint method of view, is morethe DSI suitable method for is hardnessmore suitable testing. for hardness testing. 4.2.2. Elastic Modulus 4.2.2. Elastic Modulus Through formula 9 in Section 2.2.2, it can be seen that the calculation of elastic modulus of Through formula 9 in Section 2.2.2, it can be seen that the calculation of elastic modulus of specimen is based on the known properties of testing indenter, ν and E . The elastic modulus E of specimen is based on the known properties of testing indenter, 𝜈i and 𝐸i . The elastic modulus E of material calculated from indentation experiments can be performed as follows: material calculated from indentation experiments can be performed as follows: 11−𝜈ν2 E = − (13) 𝐸= 1 ν2 11 +1−𝜈− i (13) Er + Ei 𝐸 𝐸

InIn thethe casecase ofof non-ambient temperature situation,situation, the error of calculated elastic elastic modulus modulus ξ𝜉E cancan bebe performedperformed asas follows:follows: 1 ν2 1 − i0 1Er −1−𝜈Ei0 ξE = − 1 (14) 𝐸 𝐸2 1 1 νi − 𝜉 = − −1 (14) 1Er 1−𝜈Ei −− 𝐸 𝐸 where νi0 and Ei0 are Poisson’s ratio and elastic modulus of indenter at RT, respectively. The value of νwherei0, νi, andνi0 andEi are Ei0 consideredare Poisson’s as ratio constants. and elastic modulus of indenter at RT, respectively. The value of νi0, νiThe, and calculated Ei are considered percentage as constants. error of elastic modulus induced by modulus variation of sapphire indenterThe iscalculated presented percentage in Figure 14error[ 33 ,of59 elastic]. The errormodulus increases induced from by negative modulus to variation positive of value sapphire with temperatureindenter is presented increasing in from Figure low 14 to high[33,59]. temperature. The error increases More interestingly, from negativeξE performs to positive much value higher with in

temperature increasing from low to high temperature. More interestingly, 𝜉 performs much higher in specimen with high elastic modulus. At the condition of 200 GPa, the percentage error value can reach 3.22% at 850 K and −0.52% at 50 K, respectively, illustrating that considerable error occurs in elastic modulus calculation of hard brittle materials. Thus, the influence of elastic modulus variation of tip at non-ambient temperatures should be carefully considered.

Micromachines 2020, 11, 407 15 of 25 specimen with high elastic modulus. At the condition of 200 GPa, the percentage error value can reach 3.22% at 850 K and 0.52% at 50 K, respectively, illustrating that considerable error occurs in elastic − modulus calculation of hard brittle materials. Thus, the influence of elastic modulus variation of tip at non-ambientMicromachines 2020 temperatures, 11, x should be carefully considered. 15 of 25 Micromachines 2020, 11, x 15 of 25

Figure 14. Percentage error of calculation elastic modulus at different temperatures [33]. FigureFigure 14. PercentagePercentage error error of of calculation calculation elastic modulus at different different temperatures [[33].33]. 4.3. Influence from Specimen 4.3. Influence Influence from Specimen The most common influence on the specimen is the occurrence of ice under circumstances of a waterThe vapor most containing common environment,influence influence on the which specimen is an apparent is the occurrence phenomenon of ice on under the surface circumstances of specimen, of a wateras shown vapor in Figurecontaining 15a. Theenvironment, thickness ofwhich the ice is occuan apparent rred on thephenomenon free surfaces on of the the surface surface specimen of of specimen, specimen, increases aswith shown temperature in Figure decreasing 15a.15a. The The thickness thickness and time of of passing the the ice ice occu occurredby, anrredd it on on can the the reach free free surfacesmillimeter surfaces of of thelevel the specimen specimen in a conventional increases increases withenvironment. temperature The decreasing existence andof ice, time even passing at nano by, andanmeterd it canlevel, reach is unacceptable millimeter level in in nanoindentation a conventional environment.testing, due to The Thethe existence confusionexistence of ofof ice, obtainedice, even even at properties nanometerat nanometer of level, specimen level, is unacceptable isand unacceptable ice. Re insearchers nanoindentation in nanoindentation usually adopt testing, a testing,duevacuum to the due chamber confusion to the confusionor of sealed obtained ofchamber obtained properties purging properties of specimen with of dryspecimen and gas ice. to and Researchers prevent ice. Re thesearchers usually occurrence adoptusually of a vacuumadoptice. An a vacuumchamberenvironment chamber or sealed of 10 chamberor−2 sealedPa can purging chamber effectively with purging dryreduce gas with tothe prevent dry water gas the vaporto occurrence prevent content the of ice.andoccurrence Aneliminate environment of ice.the Anice of 2 10environmentoccurrence.− Pa can eHowever, ffofectively 10−2 Pa reduceit shouldcan theeffectively be water noted vapor reduce that content the the pressure water and eliminate vaporinside content the icesealed occurrence.and chamber eliminate However, should the icebe it occurrence.shouldpositive be to noted obtain However, that an theacceptable it pressureshould effect. insidebe noted The the gas sealedthat under the chamber pressure normal should pressureinside be the positive could sealed not to obtainbechamber dried an sufficientlyshould acceptable be positiveetoff ect.prevent The to gasobtain condensation, under an acceptable normal pressurewhich effect. is could The quite gas not under besim driedilar normal suwithfficiently pressureoxidation to preventcould in notelevated condensation, be dried temperature sufficiently which is quitetonanoindentation. prevent similar withcondensation, oxidation inwhich elevated is temperaturequite similar nanoindentation. with oxidation in elevated temperature nanoindentation.

Figure 15. Possible influences influences occurred on specimen (a) ice on the surface ((b)) internalinternal stress.stress. Figure 15. Possible influences occurred on specimen (a) ice on the surface (b) internal stress. Internal stress of specimenspecimen is anotheranother potentialpotential influenceinfluence factor on testingtesting accuracyaccuracy during low temperatureInternal nanoindentation.nanoindentation.stress of specimen With is another temperature potential decreasing,decr influenceeasing, bothboth factor thethe on specimen testing andaccuracy pedestal during perform low temperaturecold contraction, nanoindentation. and the didifferencefference With temperature ofof thermalthermal expansionex decrpansioneasing, coecoefficients bothfficients the specimen couldcould induceinduce and pedestal intenseintense perform internalinternal coldstress contraction, insideinside thethe specimen, specimen,and the difference as as shown shown inof inFigurethermal Figure 15 exb. 15b.pansion For For instance, instance, coefficients copper copper could is usually is induceusually selected intense selected as theinternal as basic the material of pedestal, with a thermal expansion coefficient of 16.7 10 6 K 1 and 10.5 10 6 K 1 at stressbasic materialinside the of specimen,pedestal, with as shown a ther malin Figure expansion 15b. coefficientFor instance, of 16.7 copper −× 10 −is−6 Kusually−1 and 10.5 selected × 10− − 6as K− −the1 at × × 6 1 basicRT and material 100 K, of respectively, pedestal, with while a ther themal value expansion of silicon coefficient (as a specimen) of 16.7 is × 2.510−6 and K−1 0.5and 10.510− ×−6 K10−−−16 atK− the1 at RT and 100 K, respectively, while the value of silicon (as a specimen) is 2.5 and 0.5× × 10 K at the RTsame and temperatures 100 K, respectively, [[59].59]. The while difference difference the value of thermaltherma of siliconl expansion (as a specimen) of the two is 2.5 connected and 0.5 units× 10− 6 could K−1 at be the a samemultiple temperatures of ten and induces[59]. The million difference PascalPascal of therma levellevel internalinternall expansion stressstress of ofof the specimen.specimen. two connected Cryogenic units glue could between be a multiplethe specimen of ten and and and pedestal pedestal induces could couldmillion reduce reduce Pascal stress stress level transf transferenceinternalerence stress to to aof acertain specimen. certain extent. extent. Cryogenic However, However, glue re-fasten re-fastenbetween is themore specimen appropriate and pedestalafter refrigeration could reduce under stress the transf circumstanceerence to aof certain mechanical extent. fixation However, to re-fastenrelease the is moreinternal appropriate stress. after refrigeration under the circumstance of mechanical fixation to release the internalThe stress. internal stress is caused by thermal expansion in horizontal direction, while the expansion in verticalThe internal direction stress could is caused induce by position thermal changi expansionng of inthe horizontal specimen direction, surface. Thewhile thickness the expansion of the inspecimen vertical and direction pedestal could varies induce with positiontemperature changi flucngtuating. of the Forspecimen a copper surface. pedestal, The the thickness changing of ratethe specimeninduced by and vertical pedestal thermal varies expansion with temperature could reach fluc overtuating. 10 nm/mm·K For a copper (10 pedestal, nm of the the vertical changing position rate induced by vertical thermal expansion could reach over 10 nm/mm·K (10 nm of the vertical position

Micromachines 2020, 11, 407 16 of 25 is more appropriate after refrigeration under the circumstance of mechanical fixation to release the internal stress. The internal stress is caused by thermal expansion in horizontal direction, while the expansion in vertical direction could induce position changing of the specimen surface. The thickness of the Micromachinesspecimen and 2020 pedestal, 11, x varies with temperature fluctuating. For a copper pedestal, the changing16 of rate 25 induced by vertical thermal expansion could reach over 10 nm/mm K (10 nm of the vertical position of · ofspecimen specimen surface surface per per 1 mm 1 mm thickness thickness pedestal pedestal and and 1 K)1 K) at at low low temperatures, temperatures, which which totally totally reflects reflects to tothe the measurement measurement of indentationof indentation depth. depth. Actually, Actually this, this expansion expansion is one is kindone ofkind frame of frame driftand drift could and couldaccumulate accumulate but not but be not stable be automaticallystable automatically over time. over Thetime. most The direct most methoddirect method to inhibit to inhibit the drift the is driftenhancing is enhancing the temperature the temperature controlling controlling to reduce to temperature reduce temperature fluctuation. fluctuation. Meanwhile, Meanwhile, setting the setting fixed placethe fixed of the place pedestal of the onpedestal the same on planethe same of the plane pedestal of the surface pedestal could surface not preventcould not the prevent thermal the expansion thermal expansionbut is helpful but to is reducehelpful the to reduce position the variation position of variation surface onof verticalsurface on direction. vertical direction.

5. Applications Applications

5.1. Metallic Metallic Materials Materials The mostmost fundamental fundamental functionality functionality of lowof temperaturelow temperature indentation indentation apparatuses apparatuses could be could hardness be hardnesstesting at testing varying at low varying temperatures low temperatures [60–62]. Yoshino[60–62]. etYoshino al. conducted et al. conducted indentations indentations on a series on ofa seriesmetallic of materialsmetallic materials at temperatures at temperatures from RT tofrom LHe RT temperature to LHe temperature [63]. Their [63]. data Their of austenitic data of austenitic stainless stainlesssteels are steels shown are in shown Figure 16in ,Figure where 16a, the observedwhere the hardness observed is plottedhardness as is a functionplotted as of a temperature. function of Thetemperature. data clearly Theshows data clearly that all shows of the that hardness all of the of hardness austenitic of stainlessaustenitic steels stainless first steels increases first increases and then anddecreases then decreases with temperature with temperature decreasing, decreasing, and then further and then increases further below increases ~ 50 K. below A peak ~ value 50 K. occurs A peak in valuethe range occurs between in the 50 range K and between 100 K. This 50 isK due and to 100 the K. inhibition This is ofdue extension to the inhibition of dislocations of extension beneath theof dislocationsindentation regionbeneath by the low indentation temperatures, region and theby low plastic temperatures, deformation and mode the transforms plastic deformation from dislocation mode transformsto twinning. from Meanwhile, dislocation a phenomenonto twinning. Meanwhil of ridges occurse, a phenomenon inside the residualof ridges impressions occurs inside at lowthe residualtemperatures, impressions which isat consideredlow temperatures, as the external which is expression considered of as twinning the external occurrence. expression The of ridges twinning also performoccurrence. most The clearly ridges at also temperature perform most range clearly between at temperature 45 and 150 K,range and between turns indistinct 45 and 150 both K, withand turnstemperature indistinct increasing both with and temperature decreasing. increasing and decreasing.

Figure 16. TemperatureTemperature dependence of hardness for austenitic stainless steels [[63].63].

However, the structure of the ridges of austenitic stainless steel beneath the indentation surface However, the structure of the ridges of austenitic stainless steel beneath the indentation surface was not determined directly. This work was demonstrated by Wang et al., who conducted indentation was not determined directly. This work was demonstrated by Wang et al., who conducted experiments on monocrystalline copper with spherical indenters at temperatures ranging from RT to indentation experiments on monocrystalline copper with spherical indenters at temperatures ranging 150 K [64]. Ridges only occurred distinctly at 150 K and distributed strictly along the intersecting lines of from RT to 150 K [64]. Ridges only occurred distinctly at 150 K and distributed strictly along the intersectingslip plane and lines specimen of slip surface,plane an asd shownspecimen in Figure surface, 17a. as The shown subsurface in Figure region 17a. of The the subsurface ridges is shown region in ofFigure the ridges17b, indicating is shown that in Figure only monocrystalline 17b, indicating structure that only occurred monocrystalline at 150 K. The structure ridges wereoccurred considered at 150 K.as innerThe ridges slip bands were simplyconsidered caused as byinner increased slip bands hardness simply of caused material by with increased temperature hardness decreasing of material and with temperature decreasing and a characteristic of accumulation of geometrically necessary dislocations (GNDs). The inner slip bands resisted the flattening under high pressure and remained after the unloading process.

Micromachines 2020, 11, 407 17 of 25 a characteristic of accumulation of geometrically necessary dislocations (GNDs). The inner slip bands resistedMicromachines the flattening2020, 11, x under high pressure and remained after the unloading process. 17 of 25 Micromachines 2020, 11, x 17 of 25

FigureFigure 17. 17. Morphology Morphology of ofof (110) (110)(110) copper coppercopper indentation indentationindentation at atat 150 150150 K. K.K. ( (a(aa)) )SEM SEM SEM result. result. result. ( (b(bb)) )TEM TEMTEM result resultresult at atat the thethe ( (a(aa)) ) cutting direction [64]. cuttingcutting direction direction [64]. [64]. With temperature decreasing to 77 K, twinning was observed in copper by Gai et al. [65], as shown WithWith temperature temperature decreasing decreasing to to 77 77 K, K, twinning twinning was was observed observed in in copper copper by by Gai Gai et et al. al. [65], [65], as as in Figure 18a, and the dislocations were fewer than RT. More phenomena were found with condition shownshown in in Figure Figure 18a, 18a, and and the the dislocations dislocations were were fewer fewer than than RT. RT. More More phenomena phenomena were were found found with with of long time dwelling. The data shown in Figure 18b [66] exhibit grain distribution under indentation conditioncondition of of long long time time dwelling. dwelling. The The data data shown shown in in Figure Figure 18b 18b [66] [66] exhibit exhibit grain grain distribution distribution under under region of nanocrystalline copper with dwelling time at RT and 83 K, respectively. Grain growth was indentationindentation region region of of nanocrystalline nanocrystalline copper copper with with dw dwellingelling time time at at RT RT and and 83 83 K, K, respectively. respectively. Grain Grain moregrowth striking was more at LN striking2 temperature, at LN2 temperature, indicating that indicating the growth that of the grains growth is primarily of grains stress,is primarily but it isstress, not growth was more striking at LN2 temperature, indicating that the growth of grains is primarily stress, diffusion driven. The specific reason of this phenomenon is not yet clear. Meanwhile, dwelling also butbut it it is is not not diffusion diffusion driven. driven. The The specific specific reason reason of of this this phenomenon phenomenon is is not not yet yet clear. clear. Meanwhile, Meanwhile, caused hardness decrease with temperature decreasing in various grain size copper [67], which was dwellingdwelling also also caused caused hardness hardness decrease decrease with with temp temperatureerature decreasing decreasing in in various various grain grain size size copper copper more likely caused by less creep deformation during dwelling time. In general, most of the property [67],[67], which which was was more more likely likely caused caused by by less less creep creep deformation deformation during during dwelling dwelling time. time. In In general, general, most most variation and different phenomenon at low temperature of copper was due to the change of plastic ofof the the property property variation variation and and different different phenomenon phenomenon at at low low temperature temperature of of copper copper was was due due to to the the deformation mechanism: inhibition of dislocation extension. changechange of of plastic plastic deformation deformation mechanism: mechanism: inhibition inhibition of of dislocation dislocation extension. extension.

Figure 18. Low temperature indentations on copper [65]. (a) Twinning was observed at 77 K. (b) Grain FigureFigure 18. 18. Low Low temperature temperature indentations indentations on on copper copper [65]. [65]. ( a(a) )Twinning Twinning was was observed observed at at 77 77 K. K. ( b(b) )Grain Grain size under indentation at RT and 83 K [66]. sizesize under under indentation indentation at at RT RT and and 83 83 K K [66]. [66]. More monocrystalline materials with face-centered cubic (fcc) and body-centered cubic (bcc) MoreMore monocrystalline monocrystalline materials materials with with face-cente face-centeredred cubic cubic (fcc) (fcc) and and body-centered body-centered cubic cubic (bcc) (bcc) structurestructure were were indented indented by by Lee Lee et al.,et al., who who conducted conducted nanoindentations nanoindentations and an obtainedd obtained indentation indentation size structureeffect (ISE) were from indented RT to 160 by K Lee [68 ].et Theal., who data cond of (001)ucted Al nanoindentations are shown in Figure and 19 obtained, where theindentation trend of sizesize effect effect (ISE) (ISE) from from RT RT to to 160 160 K K [68]. [68]. The The data data of of (001) (001) Al Al are are shown shown in in Figure Figure 19, 19, where where the the trend trend theof the ISE ISE was was eff ectedeffected by by low low temperatures. temperatures. In In previous previous elevated elevated temperatures, temperatures, Franke Franke found found similar similar ofphenomenon the ISE was oneffected copper by and low argued temperatures. that the In higher previous dislocation elevated mobility temperatures, at higher Franke temperatures found similar leads phenomenonphenomenon on on copper copper and and argued argued that that the the higher higher dislocation dislocation mobility mobility at at higher higher temperatures temperatures leads leads toto large large GND GND storage storage volume, volume, inducing inducing different differen ISE responset ISE response at various at temperaturesvarious temperatures [69]. However, [69]. toLee large et al. GND considered storage a highly volume, significant inducing dynamic differen recoveryt ISE ofresponse dislocation at various annihilation temperatures in fcc materials [69]. However,However, Lee Lee et et al. al. considered considered a a highly highly significant significant dynamic dynamic recovery recovery of of dislocation dislocation annihilation annihilation in in fccfcc materialsmaterials atat relativerelative highhigh temperatures.temperatures. Meanwhile,Meanwhile, onlyonly bccbcc materialsmaterials werewere influencedinfluenced byby temperature variation on infinite indentation depth, H0, which was explained by the amplification in temperature variation on infinite indentation depth, H0, which was explained by the amplification in thethe intrinsic intrinsic lattice lattice resistance resistance with with temperature temperature reduction. reduction.

Micromachines 2020, 11, 407 18 of 25 at relative high temperatures. Meanwhile, only bcc materials were influenced by temperature variation on infinite indentation depth, H0, which was explained by the amplification in the intrinsic lattice Micromachinesresistance with 2020, temperature11, x reduction. 18 of 25

FigureFigure 19. 19. IndentationIndentation size size effect effect of of (001) (001) Al Al at at RT RT and and low low temperatures temperatures [68]. [68]. 5.2. Semiconductor Materials 5.2. Semiconductor Materials Semiconductor materials, especially represented by silicon, is always research focus in Semiconductor materials, especially represented by silicon, is always research focus in nanoindentation testing field for the various phase state under different high pressures. It is well nanoindentation testing field for the various phase state under different high pressures. It is well accepted that the original Si-I phase transforms into a much denser Si-II phase during the indentation accepted that the original Si-I phase transforms into a much denser Si-II phase during the indentation loading process, and then transforms into Si-III/XII (slow unloading rate) or a-Si (rapid unloading loading process, and then transforms into Si-III/XII (slow unloading rate) or a-Si (rapid unloading rate) during the unloading process, with phenomenon of pop-out and elbow, respectively [69–73]. rate) during the unloading process, with phenomenon of pop-out and elbow, respectively [69–73]. The same as other materials, phase transformation of monocrystalline silicon was both pressure- and The same as other materials, phase transformation of monocrystalline silicon was both pressure- and temperature-driven. Wang et al. conducted nanoindentations on silicon at temperatures ranging temperature-driven. Wang et al. conducted nanoindentations on silicon at temperatures ranging from RT to 210 K, finding the pop-out phenomenon gradually disappeared and substituted by elbow from RT to 210 K, finding the pop-out phenomenon gradually disappeared and substituted by elbow with temperature decreasing [74], as shown in Figure 20a. The phase state of residual impressions with temperature decreasing [74], as shown in Figure 20a. The phase state of residual impressions conducted at different temperatures was identified via Raman spectra (see Figure 20b), revealing that conducted at different temperatures was identified via Raman spectra (see Figure 20b), revealing that low temperatures inhibited the transformation from Si-II phase to Si-III/XII, and a-Si could occur even low temperatures inhibited the transformation from Si-II phase to Si-III/XII, and a-Si could occur even at a slow unloading rate, which strictly leads to pop-out at RT. at a slow unloading rate, which strictly leads to pop-out at RT. Compared with silicon, germanium is generally considered to have no phase transformation under Compared with silicon, germanium is generally considered to have no phase transformation nanoindentation with a spherical indenter at RT. However, Husto et al. found both pop-out and elbow under nanoindentation with a spherical indenter at RT. However, Husto et al. found both pop-out could occur at 0 C during the unloading process [75], as shown in Figure 20a, and with temperature and elbow could◦ occur at 0 °C during the unloading process [75], as shown in Figure 20a, and with further decreasing, which was quite similar with silicon, the probability of elbow occurrence increased temperature further decreasing, which was quite similar with silicon, the probability of elbow and substituted for pop-out phenomenon. Further TEM results (see Figure 20b) revealed that less occurrence increased and substituted for pop-out phenomenon. Further TEM results (see Figure 20b) defect propagation at low temperatures prompted the region under indenter reaching the critical revealed that less defect propagation at low temperatures prompted the region under indenter pressure and transformed into r8-Ge or a-Ge during unloading. reaching the critical pressure and transformed into r8-Ge or a-Ge during unloading. Both the investigations of monocrystalline silicon and germanium above benefitted from the Both the investigations of monocrystalline silicon and germanium above benefitted from the obtained P-h curves, which performed typical phenomena during the nanoindentation process. Besides obtained P-h curves, which performed typical phenomena during the nanoindentation process. pop-out and elbow, other phenomena, including but not limited to pop-in, creep, and serrated flow, Besides pop-out and elbow, other phenomena, including but not limited to pop-in, creep, and provided consecutive information of state variation under indentation region and critical information on serrated flow, provided consecutive information of state variation under indentation region and the behavior of materials under high pressure. By comparison, before the DSI technology was applied critical information on the behavior of materials under high pressure. By comparison, before the DSI on low temperature indentation, most investigations concentrated on the final state of the residual technology was applied on low temperature indentation, most investigations concentrated on the impressions. Khayyat et al. conducted low temperature indentations on monocrystalline silicon final state of the residual impressions. Khayyat et al. conducted low temperature indentations on through micro-hardness testing method which consisted of Raman spectra [76,77]. However, due to monocrystalline silicon through micro-hardness testing method which consisted of Raman spectra the absence of mechanical state obtained from P-h curves, the intermediate Si-II phase was mistakenly [76,77]. However, due to the absence of mechanical state obtained from P-h curves, the intermediate considered nonexistent during the indentation loading process. The information obtained from residual Si-II phase was mistakenly considered nonexistent during the indentation loading process. The impressions was not sufficient to reconstruct the specific load and unload indentation process. information obtained from residual impressions was not sufficient to reconstruct the specific load and unload indentation process.

Micromachines 2020, 11, 407 19 of 25 Micromachines 2020, 11, x 19 of 25

FigureFigure 20. LowLow temperature indentation on monocrystalline semiconductors. ( (aa,b,b)) PP--hh curvescurves and typicaltypical RamanRaman spectra spectra of of indented indented silicon silicon [74]. [74]. (c,d) P(-ch,dcurves) P-h andcurves TEM and result TEM of indentedresult of germanium indented germaniumwith pop-out with [75 ].pop-out [75]. 5.3. Ceramic Materials 5.3. Ceramic Materials Compared with metal and semiconductor materials, the low temperature indentation research Compared with metal and semiconductor materials, the low temperature indentation research on ceramic materials were focused on the fracture, which were conducted via Vickers indenter with on ceramic materials were focused on the fracture, which were conducted via Vickers indenter with micro-hardness testing method [78–80]. The most attractive and practical investigations concerned micro-hardness testing method [78–80]. The most attractive and practical investigations concerned the crack propagation path generating from indent corners and how it was affected by temperature the crack propagation path generating from indent corners and how it was affected by temperature variation. Figure 21 shows SEM figures of crack path made in yttria-stabilized zirconia at RT and 77 K, variation. Figure 21 shows SEM figures of crack path made in yttria-stabilized zirconia at RT and 77 respectively [78]. One striking feature is the distinct difference in the fracture mode, transforming K, respectively [78]. One striking feature is the distinct difference in the fracture mode, transforming from dominantly transgranular fracture to intergranular mode. This indicates that grain boundaries from dominantly transgranular fracture to intergranular mode. This indicates that grain boundaries become more brittle at low temperatures, which may be harmful to the fracture toughness. However, become more brittle at low temperatures, which may be harmful to the fracture toughness. However, the internal mechanism of the mode transformation was not clearly revealed and not extensive enough the internal mechanism of the mode transformation was not clearly revealed and not extensive to draw firm conclusions. This problem also exists in other kinds of ceramic materials, which perform enough to draw firm conclusions. This problem also exists in other kinds of ceramic materials, which different mechanisms at low temperatures. perform different mechanisms at low temperatures. On the other hand, the subsequent analysis on the regions around cracks was essential after On the other hand, the subsequent analysis on the regions around cracks was essential after indentation, including TEM, Raman spectra, and X-ray diffraction (XRD), which perform information indentation, including TEM, Raman spectra, and X-ray diffraction (XRD), which perform information at nanometer, micrometer, and millimeter level, respectively. In the yttria-stabilized zirconia work, at nanometer, micrometer, and millimeter level, respectively. In the yttria-stabilized zirconia work, researchers used TEM, finding larger transformed martensite with monoclinic structure on either side researchers used TEM, finding larger transformed martensite with monoclinic structure on either of the propagating crack at low temperatures. Meanwhile, Raman spectra was utilized to estimate the side of the propagating crack at low temperatures. Meanwhile, Raman spectra was utilized to tetragonal to monoclinic transformation within zones around cracks, and the results of XRD assisted estimate the tetragonal to monoclinic transformation within zones around cracks, and the results of to calibrate the data from Raman spectra. The combination of these subsequent analysis methods XRD assisted to calibrate the data from Raman spectra. The combination of these subsequent analysis provided direct evidence of microstructure evolution during crack propagation and even helped methods provided direct evidence of microstructure evolution during crack propagation and even researchers obtain more data for calculation. helped researchers obtain more data for calculation.

Micromachines 2020, 11, 407 20 of 25 Micromachines 2020, 11, x 20 of 25

Figure 21. Crack path induced by indentation on the surfacesurface of yttria-stabilized zirconia at (a) 293 K and (b)) 7777 KK [[78].78].

6. Summary and Perspectives Low temperature nanoindentation technique has beenbeen developed during the past three decades, from micro-hardnessmicro-hardness toto DSIDSI method,method, andand realizesrealizes temperaturetemperature downdown toto 4.24.2 KK (LHe).(LHe). SeveralSeveral coolingcooling methods have been attached to thethe conventionalconventional indentationindentation apparatus,apparatus, such as cryogeniccryogenic liquidliquid immersion,immersion, Peltier coolers, directly evaporativeevaporative cooling, and coldcold finger.finger. Each coolingcooling methodmethod hashas advantages andand disadvantages disadvantages on on variable variable temperature temperature ability, ability, temperature temperature range, temperaturerange, temperature stability, andstability, convenience and convenience of test (see of Table test2 ).(see Indentation Table 2). influenceIndentation factors, influence especially factors, contact especially thermal contact drift, havethermal been drift, considered have been and considered eliminated and during eliminated low temperatureduring low temperature nanoindentation nanoindentation testing. Based testing. on theBased according on the according apparatus, apparatus, researchers researchers conducted cond lowucted temperature low temperature indentations indentations on different on different kinds of materials,kinds of materials, and numerous and phenomenanumerous phenomena and trends wereand discoveredtrends were distinct discovered from RT.distinct However, from apart RT. fromHowever, the achievement apart from the we achievement mentioned above, we mentioned there are above, still a number there are of still perspectives a number whichof perspectives could be consideredwhich could in be future considered investigation in future of lowinvestigation temperature of low nanoindentation temperature nanoindentation technique. technique.

Table 2. Advantages and disadvantages of existing cooling methods. Table 2. Advantages and disadvantages of existing cooling methods.

CoolingCooling methods methods Advantage Advantage Disadvantages Disadvantages  HighHigh temperature temperature stability stability  ImmutableImmutable temperature temperature CryogenicCryogenic liquid liquid immersion immersion • •  NaturalNatural non-thermal non-thermal drift drift  PotentialPotential liquid liquid influence influence • •  Low cost Peltier coolers • Low cost Limited temperature control range Easy to control and quick response  • Limited temperature control Peltier coolers  • Easy to control and quick Directly evaporative cooling Large temperature control range rangeUncontrolled temperature rising response• • Cold finger High accuracy temperature control Low temperature cooling speed  • Large temperature control • Directly evaporative cooling  Uncontrolled temperature rising range Firstly, and most importantly, High the temperatureaccuracy temperature range and operability of elimination of contact Cold finger  Low temperature cooling speed thermal drift need to be improvedcontrol to realize stable nanoindentation at low temperatures and simplify the preparationFirstly, and before most nanoindentation.importantly, the temperature An improved range method and that operability could achieve of elimination the two advantages of contact simultaneouslythermal drift need is meaningful to be improved to low to temperaturerealize stable nanoindentation. nanoindentation Fromat low this temperatures point of view, and adopting simplify athe low preparation temperature before atmosphere nanoindentation. environment An improved to cool down method the specimenthat couldand achieve indenter the two may advantages become a moresimultaneously suitable method. is meaningful On the otherto low hand, temperature most of thenanoindentation. current experiments From this conducted point of nanoindentation view, adopting ata low a constant temperature temperature, atmosphere while environment temperature to change cool down during the holding specimen the indenterand indenter at a specificmay become load to a investigatemore suitable the effmethod.ect of temperature On the other variation hand, on materialsmost of underthe current complex experiments stress condition conducted has not beennanoindentation reported. However, at a constant this operation temperature, is extremely while temperature difficult to realize change as during the control holding of frame the indenter thermal driftat a specific should load be controlled to investigate within the nanometer effect of temperature level. variation on materials under complex stress condition has not been reported. However, this operation is extremely difficult to realize as the control of frame thermal drift should be controlled within nanometer level.

Micromachines 2020, 11, 407 21 of 25

Secondly, ultra-low load (µN) nanoindentation, which has been well realized at RT, is anticipated in a low temperature environment. This needs the influence generated from cooling system to be virtually eliminated to allow the load and displacement sensors to obtain data with low enough noise. The existing electrostatic driving method, atomic force microscopy (AFM), and Micro-Electro Mechanical System (MEMS) could conduct as the indentation driving device, while the latter two methods even have the ability to reach nanometer level impression. Besides load aspect, ultra-low temperature (mK) is also desirable. However, the environment of such a low temperature is usually enclosed, which is contradictory to the motion components of indentation apparatus and unfavorable for indentation sensors. Thirdly, the subsequent tests after low temperature nanoindentation need to be optimized. In the current experimental sequence, the specimen is usually taken out of the indentation environment and subsequent tests are conducted, such as SEM, TEM, XRD, and micro Raman spectra, in an ambient environment, which may cause additional property variation with temperature rising. A corresponding cooling system attached to this testing equipment, as well as transportation between indentation area and subsequent test area, is beneficial to maintain the original state of the specimen after low temperature nanoindentation, as well as enhance the credibility of experimental conclusions. Lastly, the current target in development of low temperature nanoindentation is realization of the functions which RT test has, including continuous stiffness measurement (CSM), scanning probe microscope (SPM) imaging, property mapping, and even scratch test. This will require a cooling system performing better compatibility on the additional functional modules and further reduce the thermal drift and other influence factors. Compared with standardized and relatively simple operation in RT nanoindentation, a highly skilled and knowledgeable user is still currently required to complete the variable low temperature operation. By implementing the above techniques, it is believed that low temperature nanoindentation technique will be more widespread as an advanced testing method, inheriting the rapid and high-precision properties of conventional nanoindentation technique. This will facilitate the investigation on the material behavior under both low temperature and high stress/strain conditions.

Author Contributions: H.Z. conceived and developed the ideal of this work; S.W. drifted the paper and revised the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Science Fund for Distinguished Young Scholars (51925504), National Key R&D Program of China (2018YFF01012400), National Key R and D Program of China (2018YFF01012400), Project of Basic Technical Research (JSJL2018110A001), Pre-research of equipment of the General Armaments Department (41422050301), ‘Double Ten Project of Scientific and Technological Innovation (18SS009), Program for JLU Science and Technology Innovative Research Team (2017TD—04), Interdisciplinary Research Fund of Jilin University (10183201822) and Changchun Major Scientific and Technological Project (18SS009). Conflicts of Interest: The authors declare no conflict of interest.

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