Material removal characteristics of precorroded Lu2O3 laser crystals and elastic deformation model during nanoscratch process

Tribology International 143 (2020) 106027

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Material removal characteristics of precorroded Lu2O3 laser crystals and elastic deformation model during nanoscratch process Shuohua Zhang, Xiaoguang Guo *, Zhuji Jin, Renke Kang, Dongming Guo Key Laboratory for Precision and Non-Traditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian, 116024, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Material removal characteristics Corrod Elastic deformation model Nanoscratch

At present, CMP is the only ultra-precision machining technology that can achieve global flattening. Unfortu­ nately, CMP processing efficiency is extremely unsatisfactory. Although the processing efficiency can be improved by increasing the alkaline concentration of CMP slurry, the surface quality will deteriorate rapidly due to excessive concentration. In this study, the removal characteristics of both uncorroded and precorroded Lu2O3 laser crystals were investigated based on nanoscratch tests with edge-forward Berkovich indenter. Further, the elastic deformation model considering both elastic extrusion and elastic recovery deformation was established. The origin of the microcracks was then discussed. The observed responses of surface quality were shown to depend greatly on the extent of elastic deformation prevalent during the nanoscratch and associated material removal processes.

1. Introduction Rare earth oxide laser crystals have been widely used in scintillation detectors and solid-state lasers. At present, yttrium aluminum garnet (YAG) doped with rare earth ions is the most common active medium in solid-state lasers [1]. Compared with YAG, lutetium sesquioxide (Lu2O3) laser crystal possesses the characteristics of low phonon energy, high thermal conductivity, high damage threshold, high quantum efficiency and moderate stimulated emission cross section. Therefore, it is an ideal host for high-power solid-state lasers with great potential applications [2,3]. However, Lu2O3 laser crystal is a typical hard-brittle and difficult-tomachine material [4,5]. To realize ultra-precision process of Lu2O3 laser crystal, chemical mechanical polishing (CMP) is the only technology to achieve global flattening [6]. Unfortunately, its processing efficiency is extremely unsatisfactory. Alkaline slurry can improve the efficiency of CMP, but the surface quality will deteriorate significantly as the con­ centration of the alkaline solution increases. Due to the complex process including both mechanical and chemical actions of CMP, there is no unified conclusion on its removal process at present [7]. Hence, in-depth study of the influence mechanism of alkaline environment on surface quality is of great significance for efficient and non-destructive CMP of hard and brittle materials. Scratching experiments provide an effective method for further study

of surface deformation characteristics and material removal mechanism [8–10]. But for hard-brittle materials, due to the limited slip systems available, the main deformation mechanism in macro-scale scratch tests is brittle failure [11,12]. Fortunately, during low depth of cut scratch tests, hard-brittle materials may exhibit a purely plastic mode, resulting in a smooth scratch groove. Accordingly, nanoscratch test provides a powerful technique for measuring mechanical and tribological proper­ ties of hard-brittle materials. Gu et al. [13] performed both single and double nanoscratch tests for optical glass BK7 and found that there existed a critical separation distance where the material removal volume reached its maximum. Wu et al. [14] investigated deformation behav­ iors of monocrystalline gallium arsenide (GaAs) induced by nano­ scratch, and observed lattice bending for the first time at atomic scale in semiconductor materials. Wasmer et al. [15] carried out the mechanical deformation by nanoindentation and scratching of GaAs and it showed that the low indentation velocity allowed twins to be nucleated and propagated from surface inhomogeneities. Klemenz et al. [16] discov­ ered the elastic response properties of Pt (111) under low, intermediate and high loads, respectively, by nanoindentation and scratch experi­ ments. Li et al. [17] studied the material removal behavior of diamond by nanoscratch experiment and obtained the effects of tangential and normal stress on the deformation mechanism. They found that with the increase in normal load the deformation mechanism transitioned from ductile to brittle fracture modes. Micro/nano wear experiments of

* Corresponding author. E-mail address: [email protected] (X. Guo). https://doi.org/10.1016/j.triboint.2019.106027 Received 28 June 2019; Received in revised form 9 October 2019; Accepted 16 October 2019 Available online 19 October 2019 0301-679X/© 2019 Elsevier Ltd. All rights reserved.

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silicon in humid air and aqueous KOH were performed with diamond tips to understand the wear process of silicon as a function of relative humidity and the atomic-scale removal mechanism [18–22]. Studies including molecular dynamics simulation in similar nanoscratch ex­ periments [23–28] and grinding experiments [29–32] have provided additional understanding in surface and subsurface damages. Thus far, however, studies on the effect of polishing environment on the nano­ scratch behavior of Lu2O3 laser crystal are still limited due to the complexity of CMP mechanism and the difficulty in preparing Lu2O3 laser crystal. In this study, a series of varied depths and constant depth scratch tests were performed on precorroded Lu2O3 laser crystals with different concentrations of alkaline solution. Then the scratch morphology, chipping process, and linear surface features were investigated to gain fundamental and systematic understanding of alkaline environment on surface quality by displacement sensor, scanning electron microscopy (SEM) and Nano Indenter G200. Finally, the elastic deformation model was established to further reveal the causes of microcracks.

a diamond Berkovich indenter and all measurements were done dry. A series of continuous and constant loading nanoscratch tests were carried out. In continuous loading nanoscratch, the scratch length was 100 μm, and the normal force was from 0 mN to 100 mN. In constant loading nanoscratch, the scratch length was 50 μm, as well as the normal forces were 5 mN and 15 mN, respectively. In all scratch tests, the scratch velocity was 1 μm/s and scratching direction was edge-forward. 3. Results and discussions 3.1. Material removal characteristics in varied depth nanoscratch The microscopic images of the residual scratch groove surface morphology of Lu2O3 laser crystal with uncorroded, 1% NaOH pre­ corroded, and 5% NaOH precorroded (herein referred as sample 1, 2 and 3, respectively) with higher magnification SEM images at distinct indi­ cated positions being depicted in Figs. 1–3, respectively. Plastic, tran­ sition and brittle regions are distinguished by scratch groove morphology, as shown in Fig. 1, to facilitate the comparison of distinct scratch regions. As the penetration depth increases, a smooth morphology is observed in the plastic region with only small stick–slip fluctuations [8]. The fluctuation magnitude becomes larger when nanoscratch enters transi­ tion region. In brittle region, radial cracks that generate inclining toward the scratching direction appear, as shown in Fig. 1(d) [15]. It is difficult to find radial cracks in the sample 2, but a large number of fine, straight, parallel lines that toward the scratching direction (consistent with [8]),

2. Experimental details Three Lu2O3 laser crystals with the same size of 10 mm � 5 mm � 2 mm were polished with CMP until all roughness values of the polished surfaces were less than 3 nm as measured with ZYGO. Then the samples were treated with non-corrosion, 1% NaOH corrosion and 5% NaOH corrosion, respectively. All the nanoscratch tests were performed on Nano Indenter G200 (MTS Systems Corp.) using

Fig. 1. Surface deformation characteristics of sample 1. (I) residual scratch path morphology (a-f) corresponding magnified views of the scratch path. 2

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Fig. 2. Surface deformation characteristics of sample 2. (II) residual scratch path morphology (a-c) corresponding magnified views of the scratch path.

Fig. 3. Surface deformation characteristics of sample 3. (III) residual scratch path morphology (a-c) corresponding magnified views of the scratch path.

which emanates from the groove edge, emerge at the lower edge of the groove, see Fig. 2 (a), (b) and (c). The longest one is 8 μm, as highlighted by the arrows in Fig. 2(b). Throughout Fig. 1I, Fig. 2II, and Fig. 3III, it is observed and confirmed that precorroded Lu2O3 laser crystals have a larger volume of material removed under the same positive pressure. In the cases of samples 1, 2, and 3, the maximum widths of scratch grooves are 5.36 μm, 6.42 μm, and 6.78 μm, respectively. The angles between the surface plastic flow line and the scratching direction of sample 1, 2, and 3 decrease gradually, which are 70� , 65� and 60� , respectively. The aforementioned angles indicate that the surfaces of the precorroded Lu2O3 laser crystals are more prone to plastic flow as shown in Fig. 1 (a), 4(b) and 5(b). Moreover, it shows that the chips of the precorroded material are more concentrated and closed to the edge of the scratched groove, while the chips of the uncorroded material are more dispersed and far away from the edge of the scratched groove comparing chips on sample 1,2 and 3. This phenomenon illustrates that the absorption deformation property is enhanced after corroded of Lu2O3 laser crystal. Aforementioned description and analysis seem to indicate that the

plasticity of Lu2O3 laser crystals increased after corrosion. However, it is interesting to note that although the smoothly scratch groove surface and the rare chips in the plastic region of sample 3 exhibit perfect plasticity, microcracks appeared at the edge of scratched groove as shown in Fig. 3. (a), (b) and (c). In order to further explore the changes brought about by pre-corrosion, a series of nanoscratch tests under small normal forces are performed. 3.2. Material removal characteristics in constant depth nanoscratch A variety of chips and microcracks appearances in constant depth nanoscratch tests under different normal forces are shown in Fig. 4. It is easy to see smaller chips are generated more easily after corrosion. With the load increasing, the sizes of the chips also increase. The longest shave appeared on the uncorroded crystal at 15 mN normal force. Comparing Fig. 4. I and II, Ⅳ and Ⅴ, respectively, chips of both samples 2 and 3 tend to a stacking condition attributed to a plastic flow, which obviously plays a significant role in the process of material removal in nanoscratch under such conditions. After corrosion, the pile-up height 3

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Fig. 4. Chips and microcracks morphology of scratch under different conditions. (I) sample 1 and 5 mN. (II) sample 2 and 5 mN. (III) sample 3 and 5 mN. (Ⅳ) sample 1 and 15 mN. (Ⅴ) sample 2 and 15 mN. (Ⅵ) sample 3 and 15 mN.

increases and SEM images under high magnification clearly show microcracks are again evident even at a minimum normal force of 5 mN, it is evident in Fig. 4 III and Ⅵ. When extreme pile-up occurs micro­ cracks are increased. This behavior may be attributed to the brittle deformation, which results from the scratching of indenter. A strong stress field will be generated around the indenter during scratching [11]. Moreover, Lu2O3 laser crystal has high modulus of elasticity. Hence, it is helpful to quantify the effect of elastic deformation on microcracks during scratching process.

for the first time, a nanoscratch elastic deformation model considering both the elastic extrusion in front of the indenter and the elastic recovery in the rear of the indenter is established in this study. The diagram of the contact region between the indenter and the sample is illustrated in Fig. 5. As illustrated in Fig. 5, the indenter is not strictly an ideal triangular pyramidal in shape, and the top of the indenter is circular. The definitions of the symbols used in Fig. 5 are listed in Table 1. According to Fig. 5, Δh can be expressed with Eq. (1). The projection of the contact area on the plane where the scratch direction is located can be derived with Eq. (2). The detail derivation steps are included in Appendix A. � � R 1 � cos ðβ αÞ Δh ¼ � R (1) 2 cos 12 ðα þ βÞ

3.3. Model of material elastic deformation in nanoscratch process Li et al. obtained the effect of elastic recovery on the projection area between indenter and material based on the geometric relationship [2]. However, the elastic extrusion of the material ahead of the indenter was not examined. Based on the geometric model proposed in literature [2], 4

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Fig. 5. Illustrations of the contact region between indenter and sample (after [2], Fig. 5). Table 1 Definitions of symbols. Symbol

Definition

Symbol

Definition

h

Penetration depth

Δh

hf

Residual depth

lCO

he

Extrusion deformation height

lCB

γ

Included angles between lCB and lCO Included angles between lCA and lCO Projected areas in normal direction

Sc1

The difference between triangular pyramid and spherical shape in normal direction Distance from the center of the top sphere to the top of the ideal pyramid Distance between the center of the top sphere and the scratch plane at the top of the triangular pyramid Projected areas in normal direction due to penetration Projected areas in normal direction due to elastic recovery Projected areas in normal direction due to pile-up

ζ S

Sc2 Sc3

where R is the radius of the circle at the top of the Berkovich indenter and was 100 nm in this setup. α is the angle between the horizontal plane and the leading edge of the indenter and was found to be 12.75� . β is the angle between the plane and the trailing face at 25.75� . � � �π �� �� � 1 �π pffiffi � π h þ Δh hf tan α α S ¼ 3ðh þ ΔhÞtan β þ tan 2 2 2 2 �� � �π �2 2 � π 1 þ ðh þ ΔhÞtan h þ Δh hf tan α β 2 2 2 (2)

Fig. 6. Relationship between penetration depth and normal force of uncor­ roded and precorroded crystals in nanoscratch tests.

hu ¼

143:69F 0:40 1

(3)

hp ¼

73:75F0:57 1

(4)

Obviously, the relationship between the normal force and the average contact stress can be expressed by Eq. (5) [33].

The penetration depth can be obtained through the in-situ mea­ surement system of Nano Indenter G200. It is no doubt that there is a close correlation between the normal force and penetration depth. As can be seen from Fig. 6, both the precorroded and uncorroded Lu2O3 laser crystals, penetration depth increases with the increase of normal force. Negative values represent a downward direction. The relationship between normal force and penetration depth of both samples 1 and 3 are fitted by power function Eqs. (3) and (4), respectively.

F ¼ 10 6 σp S

(5)

where, σ p is yield pressure. The relationship between yield pressure and the hardness of the metals, as described by Bowden and Tabor [34], can be described by Eq. (6).

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(6)

H ¼ 3σ p

This study carried out nanoindentation under a series of loads due to the extreme micro-hardness properties may affect the results. Then the functional relationships between micro-hardness and displacement of both samples 1 and 3 have been fitted by Eqs. (7) and (8), respectively, and as shown Fig. 7. h

(7)

h

(8)

Hu ¼ 5:84e51:71 þ 11:52 Hp ¼ 3:22e68:40 þ 10:72

The residual depth can be derived from formula (1) ~ (8), as shown in Eq. (9). vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u � �ω1 u 1 u pffiffi 3 λh1 uðh þ ΔhÞ2 3ðh þ ΔhÞcotα u 0 1 hf ¼ h þ Δh u χ ⋅ (9) u 4cot4 β 2cot2 β u h B C u tan2 β⋅@λ2 eω2 þ ϕA t

Fig. 8. Relationship between residual depth and normal force.

pffiffiffi where χ ¼ 3cot 4 α þ 12cot 3 α⋅cotβ þ 12cot 2 α⋅cot 2 β þ 2 3cot2 cot6 β, λ1 , ω1 are the coefficients of power function in Eq. (3) or Eq. (4), and λ2 , ω2 , ϕ are the coefficients of power function in Eq. (7) or Eq. (8). The residual depth data of the groove were obtained by reverse scanning of the Berkovich indenter after the nanoscratch. The measured residual depth data and the theoretically calculated residual depth curve are shown in Fig. 8. It reveals that prediction values of the residual depth are in good agreement with the experimental results, which indicate that the prediction model of the residual depth in nanoscratch test is successful. The spherical surface at the top of the indenter is simplified to a triangular surface as shown in Fig. 9(a). Then the indentation volume at different indentation depths can be obtained as shown in Eq. (10). pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi � 1 � V ¼ h SΔABC þ SΔDEF þ SΔABC ⋅SΔDEF (10) 3 � � � where, SΔABC ¼ ðh þ ΔhÞ � tan 2π � � �π SΔDEF ¼ Δh � tan 2

�

α þ tan

�π 2

�

�

α þ tan β

���2

π

β

2

� tan

���2

ΔV ¼

1 h 3

hf

��

SΔABC þ SΔDEF þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi � SΔABC ⋅SΔDEF

(11)

The elastic deformation volumes can be obtained by Eq. (11). The differences of elastic deformation volumes between sample 1 and sam­ ple 1 under same normal forces are shown in Fig. 10. It depicts the elastic deformation volumes of both sample 1 and sample 3 increase with the normal force rising. However, the elastic deformation volume of sample 3 is larger than that of sample 1 when normal force is less than 50 mN. This difference is particularly significant when the normal force is be­ tween 20 mN and 40 mN, and it reaches the maximum value of 0.274 μm3 when the normal force reaches 30 mN. The enormous elastic recovery causes large tension stresses to occur at the rear of the indenter during nanoscratching [11,35], Fig. 9. (b). In this scenario, the tensile stresses, combined with considerable compression stresses ahead of the moving Berkovich indenter, easily lead to the large shear stresses at the edges Oa and Ob of the indenter as shown in Fig. 9. (c). Microcracks will thus occur initially near the edges of the indenter. Fig. 11 shows the elastic deformation curve and the surface mor­ phologies of scratched grooves. It can be seen that the elastic deforma­ tion volume of the precorroded sample is significantly larger than that of the uncorroded sample under same normal force. The groove edge of sample 3 shows obvious microcracks while the groove edge of the sample 1 is smooth when the normal force is around 30 mN. With the normal force continues increasing, the elastic deformations increase rapidly. Microcracks occur at the groove edge of sample 1, and cracks appear at the groove edge of sample 3 when the normal force reaches 50 mN.

� tan 6π

π 6

The calculation model of deformation recovery volume can be deduced as shown in Eq. (11).

4. Conclusion The nanoscratch tests with Berkovich diamond indenter are pre­ conducted both on corroded and uncorroded Lu2O3 laser crystals. Furthermore, by utilizing optical microscope, SEM and displacement transducers, the elastic recovery volume model of materials in nano­ scratch process are established. Based on the test results and analysis, the following conclusions can be drawn: (1) After being precorroded by 1% alkali solution, the material removal rate increases, the chip length decreases and tends to be discontinuous, and the absorption deformation energy increases, which indicates that the plasticity of the material increases. (2) With normal force increasing, the material removal volume and chip length of Lu2O3 laser crystal increase in nanoscratch tests. Fig. 7. Relationship between displacement and micro-hardness. 6

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Fig. 9. (a) Three-dimensional drawing of Berkovich indenter. (b) Diagram of stress zone during scratching. (c) Diagram of stress zone around indenter.

Fig. 10. The difference elastic recovery volumes of uncorroded and corroded crystals under different normal forces. Fig. 11. Elastic deformation under different normal forces and corresponding edge cracks of scratched grooves.

Moreover, excessive alkalinity will lead to no chips but easy pileup. (3) Excessive alkalinity leads to the increase of elastic recovery vol­ ume which causes the large tensile stresses. The tensile stresses at the rear of the indenter, combined with considerable compressive stresses ahead of the moving indenter, causes microcracks to occur easily. (4) In the process of CMP, on one hand, the alkalinity of slurry should be increased to improve the polishing speed. On the other hand, excessive alkalinity of slurry should be prevented from causing surface microcracks. (5) Both the elastic extrusion and the elastic recovery during pro­ cessing have an important effect on the surface quality of mate­ rials. The proposed elastic deformation model can be used as an assistant tool for evaluating the surface quality of nanoscratch.

Declaration of competing interest The authors declare no competing interests. Acknowledgment The authors would like to express their great appreciation to Prof. William C. Tang, University of California, Irvine, USA for his guidance and collaboration during this research work. And this research is funded by the National key Research and Development Program of China (Grant No. 2016YFB110225) and the Science Fund for Creative Research Groups (Grant No. 51621064).

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Appendix A Assume that the elastic deformation height of the material in front of the indenter caused by extrusion is equal to the elastic recovery depth of the material at the rear of the indenter, that is he ¼ h

hf :

According to the geometrical relationship in Fig. 5(a), � � R 1 � cos ðβ αÞ Δh ¼ � R 2 cos 12 ðα þ βÞ lCO ¼

R cos ζ

γ¼ζ

α

ζ¼

π 2

ðα þ βÞ

S ¼ SC1 þ SC2 þ SC3 �π � π SC1 ¼ sin ðh þ ΔhÞ2 tan2 α 3 2 � � �π � π �π SC2 ¼ 2 sin tan α tan β h þ Δh hf ðh þ ΔhÞ 3 2 2 �π � � π Sc3 ¼ sin tan2 α h þ Δh hf ðh þ ΔhÞ 3 2

h þ Δh

hf

�2

tan2

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