Optimizing [alpha]-quartz monocrystals growth through robust design.

Pugna, Adrian ; Mocan, Marian ; Stefanescu, Werner 等

Abstract: The [alpha]-quartz monocrystals can be obtained exclusively through the hydrothermal growth method and due to their piezoelectrical properties are used mainly in resonators. By using Taguchi's robust design is possible to significantly reduce the necessary number of experiments for obtaining the [alpha]-quartz monocrystals dimensional stability and at the same time to attain that specific combination of the control factors which maximizes the Signal/Noise ratio. Consequently an improvement of economic efficiency of growing [alpha]-quartz monocrystals can be obtained.

Key words: [alpha]-quartz monocrystals, S/N ratio, Taguchi's robust design, relative dielectric permittivity, infrared quality factor.

1. INTRODUCTION

The principle of obtaining the [alpha]-quartz monocrystals by hydrothermal method is based on utilizing specific solvents, high temperatures and pressures, so that the nutrient (lascus) will solubilize and precipitate on the seeds placed in an hermetically sealed pressure vessel called autoclave. This method is the only one which ensures that thermodynamic stable [alpha]-quartz with piezoelectrical properties is obtained, because the temperature of 573[degrees]C (Curie point) is not exceeded. The autoclave for obtaining the [alpha]-quartz monocrystals, related equipments and also the temperature profile along autoclave generatrix are presented in figure 1. The growth process of [alpha]-quartz monocrystals is based on the convection of a saturated solution from lower autoclave chamber to the upper one and by precipitating this solution on the seeds. The convection flow, with a desired geometry, is realized by a controlled heating and by the help of an internal baffle.

[FIGURE 1 OMITTED]

2. DESIGN AND PROCESS PARAMETERS FOR HYDROTHERMAL GROWTH OF [alpha]-quartz MONOCRYSTALS

The [alpha]-quartz monocrystals growth depends on a large variety of physical, chemical and design parameters as follows: 1.Mineralizer nature and concentration--in mineralizer's presence, the solubilization is taking place;

--the mineralizer influences the growth rate of [alpha]-quartz monocrystals.

2. Autoclave filling degree--this parameter is very important because at the same temperature it determines different pressures, the pressure influencing the [alpha]-quartz monocrystals growth rate and quality.

3.Crystallization and solubilization surfaces--the crystallization on the seeds is in direct dependence with the nutrient solubilization and it is important to ensure a higher initial ratio between the seeds' surface and the nutrient's total surface.

4. Solubilization and crystallization temperatures, temperature gradient--it is necessary to select an optimal temperature difference between autoclave's chambers in order to avoid turbulences and chaotic crystallization and respectively a growth lower productivity (even in the conditions that there is a better [alpha]-quartz monocrystals quality).

5.Internal baffle opening--the correct internal baffle opening allows obtaining an optimal temperature gradient and a better crystallization with an optimal growth rate.

6.Seeds arrangement and orientation -the [alpha]-quartz monocrystals growth rate strongly depends on crystallographic orientation, in [alpha]-quartz's case the surface which develops faster is the one perpendicular on the optical axis.

3. DIMENSIONAL OPTIMIZATION

One of the scopes of [alpha]-quartz monocrystals optimization is to achieve a dimensional stability on z-direction for the growth process. Based on the experience gained by studying the parameters presented beforehand (Muscutariu et al., 1984); (Pugna et al., 2006) it has been decided that the [alpha]-quartz monocrystals growth is mainly influenced by 5 factors. It has been decided also (Pugna et al., 2006) to be studied the possible combinations in the case in which these 5 factors have 2 levels. If there are considered all possible experiments, there are necessary [2.sup.5]=64 experiments. Because it's practically impossible to accomplish such a great number of experiments (considering the duration of 24 days per experiment), it has been decided (Pugna et al., 2006), to utilize Taguchi's Robust Design, which allows through using a L8 orthogonal experimantal array (Roy, 2001); (Taguchi et al., 1999), to reduce the experiments number to 8, simultaneously allowing to study 2 interactions. For the initial experiments, it was designed and fabricated an experimental lab autoclave (Pugna et al., 2006).

The S/N ratios were calculated initially using relation (1):

S/N = 10log([[bar.y].sup.2]/[s.sup.2] - 1/n) [dB] [right arrow] max (1)

where: n--number of measurements, y--mean of measured values and s--standard deviation.

If there are considered the effects of factors and interactions on the measured values, than is sought that combination of factors and interactions which offers the thickness value of the aquartz monocrystals closest to the specified one.

By studying this combination of factors and interactions, results that there are problems with the convection flow and respectively problems with [alpha]-quartz monocrystals opaqueness. Similarly, if based on relation (1), there are considered the factors and interactions on the S/N ratio, results planarity problems for the [alpha]-quartz monocrystals which are close to the autoclave walls. If the S/N ratios are calculated based on MSD, as in relation (2), than results a combination of factors and interactions offering the optimum conditions and performance (presented in table 1).

S/N = -10log [1/n [n.summation over (i=1)] [(yi - yN).sup.2)] [right arrow] max (2)

The conditions obtained beforehand were transferred to a Pilot autoclave in which were performed 3 confirmation experiments. The third experiment was performed on a sample of 24 normal size seeds.

The conditions for this experiment were as follows: Experimental installation: 150 l Pilot autoclave; Lab autoclave filling percentage: 80%; Two heaters controlled separately Ni-CrNi thermocouples; Internal baffle opening: 60%; Solubilization temperature: 380[degrees]C; Crystallization temperature: 280[degrees]C; Seeds arrangement: Mode 1; Solvent: 0.5N NaOH; Pressure: 2500 bar; Experiment duration: 24 days; Initial seeds dimension on x/y/z directions: 160/40/2 mm; Theoretical dimension on z-direction: 25 [+ or -] 0.5 mm; Final monocrystals dimensions: Table 2; Growth speed on z-direction: 1.5 mm/day.

After performing the confirmation experiments, one can see an improvement of technical, statistical and performance conditions and also a better [alpha]-quartz monocrystals dimensional stability, as shown in Table 3.

4. ECONOMIC EFFICIENCY ANALYSIS

Quality Loss Function, defined by Genichi Taguchi, allows quantifying the consequences for manufacturer and customer regarding product quality level in financial terms. For target criteria (nominal is the best), as in the case of obtaining aquartz monocrystals dimensional stability, relation (3) is used for Quality Loss Function.

L(y) = k[[s.sup.2] + [([bar.y] - [y.sub.N].sup.2] (3)

Quality Loss Function for confirmation experiment 3 shows that for a target value of 25 mm, a tolerance of [+ or -] 0.5 mm, k = 160 and a scrap cost of 40$/unit of product, the loss before experiment was 9.56 $/unit of product and after the experiment the loss decresed significantly to 3 $/unit of product.

Considering a full factorial experience plan, there are necessary [2.sup.5+2]=[2.sup.7]=128 experiments in order to analyze 5 factors and 2 interactions. By using a L8 Taguchi orthogonal experience plan and 3 confirmation experiments, there are necessary only 11 experiments. Therefore by applying Taguchi's robust design, the duration for performing the experiments is reduced by almost 9 months with up to 95,650$ savings. For a monthly production of 200 [alpha]-quartz monocrystals, by applying Taguchi's method of establishing the optimal combination of factors and interactions, a dimensional stability is obtained, which according to Quality Loss Function brings monthly savings of 13,025$ that is 156,303$/annum.

5. CONCLUSIONS

By applying Taguchi's Robust (Taguchi, et al., 2004) design on [alpha]-quartz monocrystals growth will result a significant reduction of experiments duration and also significant savings of experimenting costs. The dimensional stability obtained through S/N ratio maximization and the brought of nominal value to target, brings according to QLF important savings. Further reasearches will try to improve physical properties of [alpha]-quartz monocrystals, (like relative dielectric permitivity and infrared quality factor) by linking them to design and process parameters. Further researches will also be extended to other types of crystals.

6. REFERENCES

Muscutariu, J. et al. (1984), Hydrothermal processes in a aqueous solution and growing of monocrystalline quartz. Annals of University from Timisoara, Physics Series, Vol., XXII.,pp. 19-24

Pugna, A. et al. (2006), Optimizing the hydrothermal growth process parameters of the [alpha]-quartz monocrystals using Taguchi's Robust Design. In : Virtual Design and Automation--New Trends in Collaborative Product Design, Weiss, Z. (Ed.) pp 327-336, Publishing House of Poznan University of Technology, ISBN 83-7143-228-3, Poznan, Poland

Roy, R.K. (2001). Design of Experiments Using Taguchi Approach: 16 Steps to Process Improvement, WileyInterscience; Har/Cdr edition, ISBN 0471361011, USA&Canada

Taguchi, G.; Chowdhury, S. & Taguchi, S. (1999). Robust Engineering: Learn How to Boost Quality While Reducing Costs & Time to Market, McGraw-Hill Professional; 1 edition, ISBN 0071347828, USA& Canada

Taguchi, G.; Chowdhury, S. & Wu, Y. (2004). Taguchi's Quality Engineering Handbook, Wiley-Interscience, ISBN 04713348, USA

Table 1 Optimum conditions and performance

 Level
Column # / Factor description Level Contribution

1. Internal Baffle 60 % 1 1.3
2. Temperature Diff. 380-280[degrees]C 1 0.108
3. Solvent NaOH 1 1.684
4. Nutrient 0.5 g/l 2 2.271
5. Seeds arrangement Mode 1 1 0.794
6. Interaction 3x5 Int 3x5 1 1.383
7. Interaction 3x7 Int 3x7 1 0.987
Total contribution from all factors 8.526 [dB]
Current grand average of performance 3.708 [dB]
Expected result at optimum condition 12.235 [dB]

Table 2 Confirmation experiment 3

 Monocrystals final dimension [mm]
Experiment 3
Column/Row 1 2 3 4 5 6

1 24.9 24.8 24.9 25.0 25.1 24.8
2 25.2 25.1 24.9 25.1 25.1 24.9
3 25.2 25.1 25.0 24.8 24.8 25.0
4 24.9 25.1 24.8 24.9 24.8 25.1

Table 3 Comparison between current, predicted and obtained conditions

Initial and
confirmation Current Predicted Pilot
experiments conditions conditions conditions

S/N Ratio 3.708 12.235 17.269
Mean 24.587 25 24.970
Standard deviation 0.505 0.189 0.136
Cp 0.999 2.669 1.785
Cpk 0.728 2.669 1.783