Mechanism of nanodiamonds in the lapping of magnetic heads

Nanodiamond, as the main component of slurry in the precision lapping process of magnetic heads, plays an important role on its surface quality. This paper studies the mechanism of nanodiamond embedded into Sn plate in the lapping process. The embedded pressure satisfies and the embedded depth satisfies . The above formulas are deduced from establishment of mathematical and physical models. AFM, SEM and AES are used to carry out surface quality detection and analysis of disk head. Results show that, both black spots on the surface and the removal rate have an important relationship with the nanodiamond. The experiments based on slurries with three different diameters （ 50 nm, 70 nm and 100 nm respectively ） of nanodiamond are conducted, and the results show a better removal rate can be obtained with 100nm diamond embedded in the plate (21 n m · min -1 ).

, and the embedded depth satisfies HV P k / 1 properties of diamond itself, but also has the special properties of nanoparticles, such as effects of small size, quantum size, surface, the macroscopic quantum tunnel [1][2].
In recent years, many scholars have done a lot of research on the stability, the continuity, and the shape, the particle size distribution, etc. of nanodiamond [3][4]. The nanodiamond aggregates easily, so the studies on dispersion of nanodiamond are particularly important, recent studies have focused on the thermodynamic stability of nanodiamond powder, dynamic stability and aggregate stability [5][6][7][8]. Many scholars have done many beneficial researches on the dispersion of nanodiamond in aqua system [9][10][11][12]. However, because of the metallic properties of magnetic head materials, lapping process requires non-aqueous system to avoid the possible existing of chemical corrosion. Dispersion of nanodiamond in nonaqueous systems directly affects the stability of its embedded in the plate, thus affecting the surface lapping quality of the magnetic head. Solid content and oil density and surface modifying agent of nanodiamond are considered to be the main factors affecting the dispersion of nanodiamond in nonaqueous systems [13][14]. Due to hard aggregation composed of Van Edward forces and hydrogen bonds, and soft aggregation caused by the surface atomic binding force, the methods to improve nanodiamond stability include: 1) Adding the surfactant to make the surface absorption or chemical reaction of the nanodiamond; 2) Using polymer nanodiamond powder instead of monomer, to avoid the particles getting too close; 3) Ultrasonic dispersion [15][16][17]. When using nanodiamond with good dispersion to preparing the slurry, it has high hardness, high heat transfer, high endurance and relatively better chemical stability [18][19][20][21]. When it is used in the lapping of magnetic heads, the surface roughness can be greatly reduced [22][23][24][25]. Some scholars believe that the improvement mechanism is because of the existing ball bearing effect between the spherical nanodiamond and Sn plate, in which friction of rolling and gliding coexist. It can significantly increase lapping endurance and reduce the friction effect [26][27]. While some scholars believe that it is because of the existing boundary lubrication among the nanodiamond, the magnetic heads and the oil, which greatly reduces the friction [28]. There are few studies on the mechanism of nanodiamond embedded into Sn plate in the lapping process. In this paper, the mechanism of nanodiamond embedment is discussed by establishing the models, the two key factors, pressure of nanodiamond embedded into plate and the best value of embeded depth is studied, which have an important effect on the lapping surface of the magnetic head, especially the black spots and materials' removal rates of magnetic heads. As shown in Fig.1 and Fig.2, SEM and AFM pictures show the black spots on the surface of magnetic heads. Black spots refer to those spots usually bigger than 10nm in diameter, round with white reflection and the diamond-like protrusion. Since the capacity of holding nanodiamonds for Sn plate is limited, the pressure and embedded depth for nanodiamonds are very important.When the nanodiamonds are under less pressure, the embedded depth will be shallow, and the number of embedded particles will be less, which is hard for the materials of magnetic head to touch the diamonds in the lapping process. The nanodiamonds embedded into the plate surface are also easy to fall off and flow along with slurry. Both of the two cases will lead to low removal rate.
When the nanodiamonds are under bigger pressure, the embedded depth will be deeper, the number of embedded particles will be more, resulting in the deformation of the Sn plate and more defects of the head surface including scratches, protrusion, recession, black holes, etc. AESE1127-08 is used to do further research on the composition of black spots, as shown in table 1. The experimental data confirmed that carbon content of the region with black spots is much higher than that of normal region. In this paper, the mechanism of embedded nanodiamond was discussed through the establishment of mathematical and physical models. The optimum value of the pressure and depth required for the nanodiamond embedment is studied deeply and using slurries with different diameters of nanodiamond to study their influences on removal rate of magnetic head materials. P , the pressure when plastic deformation begins.

Indentation depth analysis
As shown in Fig.4, according to the test method of micro hardness, indentation depth δ is decided by hardness and load, as follows:

Material preparation
Three types of nanodiamonds extracted from CKK slurry with different radii, which were used for head lapping plate preparation, have been pictured by Hitachi S4800 high resolution SEM, with Vacc 5.0 kV (As shown in Fig.5).

Machine and embedding process
Conditions: HYPREZ Lapping Machine from Engis Company, Japan was used.
As shown in Fig.6，the   Ring rotation speed kept 25 rpm﹒min -1 , the weight was 6 kg and the shaving time was 25 mins. The lubrication was AM-ZX-60 from Engis Co. Removal rates were tested through calculating the resistant of magnetic heads before and after lapping by using SSCL-F precision magnetic test machine, which was made in TDK, Japan. Table 2).

Removal rates (shown in
Removal rates are important for hard disk heads production, high removal rates are desirable, slurries with 50 nm and 75 nm nanodimonds have lower removal rate, 100 nm has normal removal rate.
Here, V--removal volume, P--pressure, H---hardness of removed materials, L---sliding distance, K1---a universal parameter decided by the friction coefficient, the shape of diamond, plate charging quality, toughness and plastic models of rowbar.

Removal rate calculation under crack deformation
Here, P---pressue, H---hardness, T---crack toughness, L---sliding distance, K2--a universal parameter decided by the shape and radius of diamond. Both mechanisms take effect in the material removal. However, equation  and  show that the removal volume will increase if we raise the pressure (P) and sliding distance (L) is raised. Removal rate rises while weight increases. And when the plate speed is raised, L in unit lapping time increases, leading to the increase of removal rate.

Summary
The mechanism of nanodiamonds embedded into Sn plate has been discussed in this paper.

Acknowledgements
This work is supported by the lapping laboratory of SAE Technologies Declarations： a. Funding (information that explains whether and by whom the research was supported) The research leading to these results received funding from DGUT Ph.D. funding.

b. Conflicts of interest/Competing interests (include appropriate disclosures)
Not applicable c. Availability of data and material (data transparency) The authors confirm that the data supporting the findings of this study are available within the article. The raw data are available from the corresponding author upon a request.       Modeling of single diamond indentation depth Lapping machine for nanodiamonds embedded into plate