Surface Layer of a Polished Crystal Plate

Fukuyo, H.; Oura, N.

doi:10.1109/freq.1976.201322

Cited by 10 publications

(4 citation statements)

References 1 publication

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“…The depth of etch at which the rate is determined principally by the orientation was estimated (Table Ill) from these curves for the various faces. As this depth of etch is usually [27] identified with the thickness of the disturbed layer created by the initial mechanical lapping [10,[27][28][29] the results displayed in Table II! suggest that the disturbed surface layer is not only a function of the abrasive particle size but is also sensitive to the crystal orientation.…”

Section: Discussionmentioning

confidence: 99%

Topography of etched rhombohedral faces of quartz crystals: evidence for orientation effects

1986

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A study has been made of the rate at which the rhombohedral faces of a natural quartz crystal are etched in a concentrated ammonium bifluoride solution. The thickness of the disturbed surface layer created by an initial mechanical lapping is estimated from rate data. The etching rate as well as this thickness are found to be sensitive to natural face orientation. The changes in the surface texture of the rhombohedral faces with repeated chemical etchings are investigated. The variation in the roughness parameters with the average depth of etch shows both directional and orientation effects. The chemical attack results in the formation of stable etch figures characteristic to the orientation of the surface on which they lie and which enlarge with repeated etchings. Finally, schematic etch figures are proposed for the differently oriented rhombohedral faces. IntroductionChemical etching of quartz plates in HF or in NH4F" HF solutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] can constitute a convenient procedure to develop high frequency quartz resonators [8][9][10][11][12][13][14][15][16][17][18]. Hence in the past few years many experiments on cuts commonly used for stable quartz crystal resonators, such as the AT-cut [8 13], the BT-cut [12][13][14] and the SC-cut [14-18], have been carried out. Some of these experiments [12,13,15,16,[18][19][20] provided evidence for a formation of final dissolution figures depending on the crystal orientation in agreement with other works [3,[21][22][23] showing that the etch method can constitute a chemical means of determining the crystal symmetry.In terms of the structural effect previously proposed by Ernsberger [1] to explain the variation of the dissolution rate of quartz plates with the crystal orientation, the dissolution mechanism is primarily determined by the atomic arrangement at the exposed surface of a quartz specimen. Moreover, the growth of a quartz crystal results in the development of natural rhombohedral faces intimately connected with the symmetry and the structure of this crystal. Thus a detailed study of the etching of such natural faces can perhaps permit a better understanding of the structural effect in chemical etching of quartz plates. To our knowledge there is an almost complete lack of experimental work devoted to the systematic study of the formation of etch patterns on the rhombohedral faces of quartz crystals. Hence, the purpose of this paper is to report investigations of the changes with prolonged etching in the surface topography of quartz plates whose orientations are the same as those of natural faces.

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Section: Discussionmentioning

confidence: 99%

Topography of etched rhombohedral faces of quartz crystals: evidence for orientation effects

1986

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“…Katz, Cheng, and Aula [4] proposed a solution to this problem 1 using node voltage measurements with a voltage source connected between 0 and G, where the symbol k denotes node k. They showed that although, in theory, measurement of two node voltages should suffice, accuracy and sensitivity ^ problems require many additional measurements. In this paper, we present several alternative methods for solving the problem, all based on resistance measurements.…”

Section: Equation (4) Expresses the Drift Rate Shown Inmentioning

confidence: 99%

“…In Section III, we 1 Unlike the network of Fig. 1 (a), Katz et al [4] assumed the end resistances to be the same as any internal series resistance. This does not significantly change the problem and methods for locating fault in Fig.…”

Section: Equation (4) Expresses the Drift Rate Shown Inmentioning

confidence: 99%

Effect of the worked layer in quartz-crystal plates on their frequency stabilities

Oura

Kuramochi

Matsuda

et al. 1981

IEEE Trans. Instrum. Meas.

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This paper describes the direct measurement of the relation between the worked layers in quartz-crystal plates and their effect on the frequency stability. The rectangular fundamental 5-MHz A T-cut specimen plates lapped and polished with emery powder and cerium oxide, respectively, were placed in gap-type holders and con nected with oscillator circuits, and their frequency stabilities were measured. The frequency stabilities are evaluated by the fractional frequency deviation to the nominal frequency ratio, power spectral density, and the Allan variance. The main results are: 1) The frequency drift due to the worked layer is dealt with as a relaxation process. It can be approximated by a sum of one to three terms of an exponential function.2) The depth of the worked layer has a large effect not only on the long-term frequency stability but on the medium term in the Fourier frequency range of 10~3 to 10~" 7 Hz. 3) It does not have a dominant effect on the short-term stability with an averaging time of less than 10 s. I. INTRODUCTION I T IS CONSIDERED that the worked layer in the quartzcrystal blank caused by the lapping and polishing process has a large influence on frequency stability, when the crystal units are used in oscillators. With respect to this layer, many studies have been made from the viewpoint of the precision polishing of the thin quartz plate [1]. Vig and others show in detail the effect of lapping and polishing on the quartz plates and their cleaning methods by examining with the electron scanning microscope and surface analyzing instruments, etc. [2], [3]. The authors have also reported on the polished layer [4] and the refractive index distribution normal to the polished surface of the fused quartz observed by ellipsometry [5]. However, most of the studies have placed their emphasis on the obser vation of the surface roughness and the measurement of the depth of the layer. Measurement has not been made on the correlation between the frequency stability and the processing condition. In this paper, the authors try to clearly show such a correlation. Crystal units were made by using the same gap-type holders and crystal blanks having the same geometry and angle of cut, finished with various grain-size abrasives. Crystal oscillators were made by using the same type oscillator circuit and ovens for each specimen. The long-, medium-, and short-term fre quency stabilities were measured with the measure oidf/f, the power spectral density, and the Allan variance, respectively, Manuscript received July 7, 1980. The authors are with the Research f a 5 MHz x.r U.9mm ye= 0.334 mm Y z. = 16.0 mm β= 35 β 15'

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“…Interest in chemical etching as a procedure to prepare high-frequency quartz resonator plates [1][2][3][4][5][6][7][8][9][10][11][12][13][14] with clean and smooth surfaces has been revived in the past few years. The possibility of a chemical polishing of quartz surfaces by immersion in NH4HF solutions or in NH4F with HF mixture has been investigated and some satisfactory results have been obtained on ATcut [1,2,7,8] and SC-cut [5,6,14] quartz plates.…”

Section: Introductionmentioning

confidence: 99%

Dissolution shapes ofY-rotated quartz plates andY sections derived from the polar diagram of the dissolution slowness

1989

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A study has been made of the rate at which various Y-rotated quartz plates are etched in a concentrated ammonium bifluoride solution. The changes in the surface texture of these differently oriented plates on repeated etching are systematically investigated. To obtain all the information needed for an analysis of the dissolution shapes in the framework of the tensorial representation of the dissolution slowness the profile graph of a deeply etched Y-cut plate is also reported. The polar diagram Lxz(O) of the dissolution slowness associated with the Y-rotated quartz plates is then derived using profile graph data. Numerical and graphical simulations of the dissolution shapes are used to verify the adequation of the law Lxz (0). The comparison of the theoretical etch profiles with the Z" etch profiles produced by repeated etching on some Y-rotated quartz plates shows complete agreement. Excellent agreement is also found between the theoretical and experimental shapes of the magnified profile graph related to deeply etched Y sections. From the consistency between the observed dissolution shapes and the computed shapes deduced from the tensorial analysis of the dissolution we can conclude that the proposed polar diagram Lxz(O ) represents accurately the variations of the dissolution slowness with the angle 0 in the XZ plane.

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Surface Layer of a Polished Crystal Plate

Cited by 10 publications

References 1 publication

Topography of etched rhombohedral faces of quartz crystals: evidence for orientation effects

Topography of etched rhombohedral faces of quartz crystals: evidence for orientation effects

Effect of the worked layer in quartz-crystal plates on their frequency stabilities

Dissolution shapes ofY-rotated quartz plates andY sections derived from the polar diagram of the dissolution slowness

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