Shock-wave induced mechanoluminescence: A new technique for studying effects of shock pressure on crystals

Author’s Accepted Manuscript Shock-wave induced mechanoluminescence: A new technique for studying effects of shock pressure on crystals B.P. Chandra, S. Parganiha, V.D. Sonwane, V.K. Chandra, Piyush Jha, R.N. Baghel www.elsevier.com/locate/jlumin

PII: DOI: Reference:

S0022-2313(15)30284-2 http://dx.doi.org/10.1016/j.jlumin.2016.05.046 LUMIN14017

To appear in: Journal of Luminescence Received date: 21 July 2015 Accepted date: 24 May 2016 Cite this article as: B.P. Chandra, S. Parganiha, V.D. Sonwane, V.K. Chandra, Piyush Jha and R.N. Baghel, Shock-wave induced mechanoluminescence: A new technique for studying effects of shock pressure on crystals, Journal of Luminescence, http://dx.doi.org/10.1016/j.jlumin.2016.05.046 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Shock-wave induced mechanoluminescence: a new technique for studying effects of shock pressure on crystals B.P. Chandra1, S. Parganiha1, V.D. Sonwane1, V.K. Chandra2, Piyush Jha3*, R.N. Baghel1 1

School of Studies in Physics and Astrophysics, Pt. Ravishankar Shukla University, Raipur

492010 (C.G.), India 2

Department of Electrical and Electronics Engineering, Chhatrapati Shivaji Institute of

Technology, Shivaji Nagar, Kolihapuri, Durg 491001 (C.G), India 3

Department of Applied Physics, Raipur Institute of Technology, Chhatauna, Mandir Hasuad,

Raipur 492101, (C.G.), India 

Corresponding author. Tel.: +91 9179964940. Email: [email protected]

Abstract The impact of a projectile propelled to velocities in the range of 0.5-2.5 km/s on to a target (Xcut quartz crystal) produces shock waves travelling at velocity of nearly 10 km/s in target, in which intense mechanoluminescence (ML) pulses of microsecond duration are produced, both in compression and post-compression conditions. The piezoelectric field produced due to surface charges of fractured target, causes band bending and subsequently, the free charge carriers are generated in the respective bands and the emission of ML occurs. The ML appears after a delay time tth whose value decreases with increasing value of the shock pressure. Initially, the ML intensity increases with the shock pressure because of the creation of more surfaces; however, for higher values of the shock pressure, the ML intensity tends to attain a saturation value because of the hardening of the crystals due to the creation of small crystallites in which the creation of new surfaces becomes difficult. The ratio between peak ML intensity in the 1

uncompressed region and the maximum ML intensity in the compressed region decreases with increasing shock pressure because more defects produced at high pressure generate higher barrier for the relaxation of blocked cracks under compression. The expressions derived for characteristics of shock-induced ML are able to explain satisfactorily the experimental results. Shock-wave velocity, shock pressure, transit time, lifetime of electrons in conduction band, etc. can be determined by the shock-induced ML.As such, the shock-induced ML provides a new optical technique for the studies of materials under shock pressure.

1. Introduction A shock wave is a type of propagating disturbance. It is defined as an extreme compression wave that propagates with supersonic velocity, abruptly compresses, heats, and plastically deforms the solid matter. In this way, the shock waves are fundamentally different from seismic (elastic) waves. Practically, the transient high pressures are produced using powerful sources of energy such as kinetic energy from the impact of high speed projectiles, chemical energy from the detonation of high explosives, kinetic energy from pulsed atomic particles, optical energy from pulsed lasers, or nuclear energy from neutrons or X-rays, etc. [13]. In these processes, the time of load is extremely short, and consequently, the initial stress wave steepens immediately to an almost atomically sharp discontinuity, which separates highly compressed material from uncompressed material. In general, the shock-induced physical and chemical changes occurring in minerals are collectively called shock effects or shock-metamorphic effects. This term is relatively broad and it covers any type of shock-induced changes such as phase-transformations, formation of lattice defects, decomposition reactions and resultant changes in physical and chemical properties of 2

materials. Using different techniques such as spectroscopic techniques, X-ray diffraction, optical microscopy, etc., a great diversity of natural shock effects has been studied and reported till now [1-10]. In fact, the physical nature of some of the effects was not completely understood and others were not even known to researchers until transmission electron microscope (TEM) was used to characterize the mineralogical effects at the nanometer range. On the basis of the TEM observations, the following simple subdivision of shock effects and processes occurring during shock compression and decompression has been proposed [11]: (i) Deformation: formation of dislocations, planar microstructures (planar fractures and planar deformation features), mechanical twins, kink bands, and mosaicism, (ii) phase transformations into high-pressure phases and diaplectic glass, (iii) decomposition into a solid residue and a gaseous phase, and (iv) melting and vaporisation of entire mineral (subsequently quenched as shock-fused glass or polycrystalline aggregates). Other factors influencing shock deformation include bulk rock density, porosity, modal mineral composition, crystallographic orientation relative to the shock wave and shock impedance contrast between adjacent minerals [12-14]. Brooks [15] have reported the shock-induced mechanoluminescence (ML) from fused and crystalline quartz. He has suggested that the luminescence in quartz shocked parallel to the X axis is caused by the combined effects of piezoelectric voltage and shock compression. The light observed in crystalline quartz shocked parallel to the Y and Z axes and in fused quartz is attributed to mechanoluminescence. Brannon et al. [16] have made the spatial and spectral studies of shock-induced luminescence from X-cut crystalline quartz as a function of stress level. They have reported that the shock-induced luminescence spectra from X-cut crystalline quartz are band-like rather than blackbody spectrum. Similar results have also been obtained by Brannon et al. [17] for the shock-induced luminescence from Z-cut lithium niobate crystals.

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Thus, for low shock pressure, the shock induced light emission in quartz and lithium niobate crystals arises due to the luminescence. The present paper reports that the shock-induced mechanoluminescence provides a new technique for the studies of the effects of shock pressure on crystals. The significances of present study are as given below: (i) Although some experimental results are available for shock-wave induced ML, the salient features of shock-wave induced ML have not been understood till now. (ii) Till now ML has been studied for the strain rate of 1 sec-1 [18-21], in which the ML response time is in the millisecond range. In the shock-wave induced ML the strain rate is very high on the order of 104 sec-1, in which the ML response time is in the microsecond range [16,17]. (iii) In the shock-wave induced ML both the prompt ML and delayed ML appear, the appearance of prompt and delayed ML has not been understood till now. (iv) The possible uses of the shock-wave induced ML have not been reported till now by the researchers. (v) The dependence of the characteristics of shock-induced ML on different factors has not been understood. (vi) The shock-induced ML may be useful for understanding the earthquackes and earthquake lights. The present paper explores the salient features of shock-induced ML for the first time. The expressions derived for the characteristics of shock-induced ML are able to explain satisfactorily the experimental results.

2. Mechanism of shock-induced mechanoluminescence of quartz crystals The ML of quartz crystals can be understood with respect to the following points: (i)

The onset of fracture and onset of ML in quartz crystals take place simultaneously [16]. Thus, the ML in quartz crystals takes place during the creation of new surfaces by fracture of crystals.

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(ii)

Quartz crystals are non-centrosymmetric [22, 23] and their piezoelectric constant d11 =2.37 x10-12 C N-1, Young modulus of elasticity =99.45 GPa [24], and stress near crack-tip= Y/100=0.994 GPa=0.994x109 Nm-2. Thus, the surface charge density near the crack-tip, σ=2.37 x10-12x0.994x109= 2.355x10-3 Cm-2. The electric field F between the oppositely charged surfaces will be, F=σ/ε0, where ε0 is the permittivity of free space, which is equal to 8.85×10-12 C2N-1m-2. Thus, an electric field on the order of 2.66x106 V cm-1 may be generated between the newly created oppositely charged surfaces. Since the Young’s modulus of elasticity increases many times due to the applied high shock pressure [25], a piezoelectric field on the order of 107 V cm-1 may be produced near the charged surfaces of crystals [26-29]. As the energy gap for wide-gap semiconductors and insulators is significantly larger, for the electric field on the order of 107 V/cm, the electrons may not tunnel from valence band to the conduction band; however, the probability of field ionization of localized states such as impurity centres (acceptors and donors) or other effective mass- like species (donor–acceptor pair states) may be much higher [30].Consequently, during the creation of new charged surfaces of a crystal a large number of free electrons and holes may be generated in the in the conduction band and valence band of the crystals.

(iii)

Subsequently, the capture of electrons by the luminescence centres may give rise to the light emission. Also, the energy released during the electron-hole recombination may cause the luminescence excitation. The electron bombardment on the surface of crystals may also cause luminescence, but such contribution may be less as compared to the number of electron trapping in the luminescence

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centres because the number of electrons being ejected from the newly created surfaces will be comparatively less.

3.Mathematical approach to the shock-induced mechanoluminescence of quartz crystals The spectral and spatial characteristics of shock-induced luminescence of X-cut quartz crystals have been studied by Brannon et al. [16] in the stress range 4.7-28 GPa, in which planar shock waves were generated in the specimen by using a single-stage light -gas gun to produce plane impact loading of the specimen. Both fast- framing photography and five-channel optical pyrometry were used to observe the luminescence. The framing photography indicated that the emission pattern is heterogeneous for stresses just above the dynamic yield point. A further increase of the stress resulted in a pattern which was essentially homogeneous. Spectra from Xcut quartz are band-like rather than black body. The crystalline X-cut quartz has emission peaks near 400 and 600 nm; a change in the 400 nm emission with time can be correlated to wave interaction times. Narrowband filters and photomultiplier tubes were used in the optical pyrometry experiments. During the impact of projectile moving with a velocity in the range of 1 km/s on the target (quartz crystal) a shock-wave moves through the target and subsequently the target gets fractured. If Us is the velocity of shock-wave and A the cross-sectional area of the target, then the rate of increase of compressed volume, dV/dt, of the target is given by dV  AUs dt

…(1)

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If K is the correlating factor between the rate of creation of new surfaces, dS/dt and , dV/dt=AUs, the rate of volume compressed by the shock-wave; then the creation of new surface area can be expressed as dS  KAUs dt

…(2)

If Ψ is the number of electrons produced during the creation of unit surface area of the crystal, then the rate of generation of filled electrons is given by G

dS  KAUs dt

…(3)

If τe is the lifetime of electrons in the conduction band, then we can write the following rate equation dn dn G  KAUs  n dt e

….(4)

where n is the number of filled electron traps at any time t, and β = 1/τe. Now, integrating Eq. (4), we find n exp(t ) 

KAUs exp(t )  C 

…(5)

where C is the constant of integration. Taking n=0, at t=tth, where tth is the threshold time at which the pressure attains the threshold value for the appearance of ML, we get C

KAUs exp(t h ) 

…(6)

From Eqs. (5) and (6), we get n

KAUs [1  exp{( t  t th )}] 

….(7)

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If η is the efficiency of photon emission during the capture of electrons in luminescence centres, then the ML intensity I can be written as

I  n  KAUs [1  exp{(t  t th )}]

…(8)

(i) Rise of ML intensity in the transit region For β (t-tth) << 1, Eq. (8) can be expressed as

I r1  KAU s  (t  tth )

…(9)

It is seen from Eq. (9) that, when the moving projectile makes an impact on the crystal, the ML will start appearing at tth, and then it will increase linearly with time. (ii) Saturation value of the ML intensity For significant duration of time β (t-tth) >> 1, from Eq. (8), the saturation value of the ML intensity is given by

I ts  KAU s

...(10)

(iii) Value of the ML intensity It at the transit time tt For the small thickness of the sample, the saturation value could not be achieved. In this case, using Eq. (8), the ML intensity at the transit time is given by

I t  KAU s [1  exp{ (tt  tth )}]

… (11)

(iv) Decay of ML intensity after tt The shock-wave disappears at the transit time t=tt, and therefore, Us=0, at t=tt. Thus, using Eq. (4), we get, dn/dt=-βn,. Now, following the previous procedure for the derivation of equation for the ML intensity, the decay of ML is given by

I d1  KAU s exp[- (t - t t )]

….(12)

As the ML again starts after tt, there will be overlapping between decay of ML intensity after tt and rise of ML intensity after tt, and thus the effective decay after tt can be written as 8

I d 1 I r 2  I pt exp[- (t - t t )]

…(13)

where Ir2, is the rise of ML intensity Ipt in the post-transit region whose extrapolated value starts at tt. Equation (13) indicates, that after tt, (Idl-Ir2) should decrease exponentially with time , in which the slope will be equal to β, and the lifetime of electrons will be τe=1/β. (v) Rise of ML intensity in the post-transit region The shock-wave pressure disappears at the transit time, t=tt , and therefore, the shock pressure in the sample or the piezoelectric charges on the surface of the crystals relaxes. In this case, newly created charged surfaces of the crystals are again created and then again the rise of the ML intensity takes place with time. After the transit time tt, the shock wave disappears and then some of the cracks blocked by the barriers become able to move. If the area of new surface created at any time after a time tc, is S, and τr = 1/α , is the rise time of the newly created surfaces, then we can write the following equation

S  S0 [1  exp{(t  t c )}]

…(14)

where S0 is the total area of newly created surfaces in the post transit region. Now, using Eq. (14) the number N of electrons in the conduction band at any time t is given by

n  S0 [1  exp{(t  t c )}]  n 0 [1  exp{(t  t c )}]

…(15)

where n0=ΨS0. From Eq. (15) the rate of generation in the conduction band is given by

G  n 0 [exp{(t  t c )]

…(16)

In this case, using Eq. (16), we can write the following rate equation

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dn  n 0 exp[ ( t  t c )]  n dt

…(17)

Integrating Eq. (17) and taking n=0, at t=tc , we get

n

n 0 [exp[ ( t  t c )  exp[ ( t  t c )]] (  )

….(18)

Now, for ξ>>β, the ML intensity is given by I  n 

n 0 [exp[ ( t  t c )  exp[ ( t  t c )]]   

…(19)

For β (t-tc) << 1, and ξ (t-tc) << 1, Eq. (19) can be written as

I  n 0 (t  t c )

….(20)

Equation (20) indicates that, after tc, the ML intensity should increase linearly with time. (vi) Time tmp corresponding to the ML peak in the post-compression region It is evident from Eq. (19) that I=0 for (t-tc)=0; and for (t-tc)=  , and therefore, I should be maximum for particular value of time tm. Differentiating Eq. (19) and equating it to zero, the time tmp, at which the ML intensity will be maximum in the post-deformation region, can be expressed as

t mp  t c 

1  ln( )     

…(21)

From Eqs. (19) and (21) the maximum ML intensity at Imp , (for β'>>β) , is given by I mp 

n 0  n 0 

….(22)

Now integrating Eq. (19) the total ML intensity in the post-deformation is given by

I Tp 

n 0 

…(23)

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(vii)

Intensity Id2 corresponding to the ML peak in the post-compression region From Eq. (19), for ξ>>β, the decay of the ML intensity after tmp can be expressed as

I d 2 I 02 exp[ (t  t mp )]

…(24)

where I 02 is the value of Id2 at t=tmp. (viii) Pressure dependence of It and Imp When the shock-waves move, more compression of the crystal takes place, and therefore, the crystal becomes more hard. In this case, it becomes difficult to further compress the crystal. If χ is the attrition coefficient, then the rate of generation of new surfaces with shock pressure P can be expressed as dG  G 0  G dP

…(25)

where G0 is the value of G for low compression of the crystals. Integrating Eq. (25) and taking G=0, at P=Pth, we get

G  G 0 [1  exp{(P  Pth )}]

…(26)

where Pth is the threshold pressure for the ML emission. Equation . (26) shows that G tends to attain a saturation value for higher values of P. Consequently, the ML intensity will also tend to attain a saturation value for higher values of P, and we can write

I ts  I10[1  exp{(P  Pth )}]

…(27)

where I10 is the saturation value of Its, Similarly, the equation for Imp can be written as I mp  I 20[1  exp{(P  Pth )}]

…(28) 11

where I20 is the saturation value of Imp, and  is the attrition coefficient for the increase of Imp with increasing pressure. (ix) Burst in radiance versus time curves After tt=0, both the ML intensity due to the decay of ML as well as the ML intensity due to the rise of ML intensity in the post-transit region are observed. Therefore, a burst appears at tt. (x)

Ratio between Imp and It Using Eqs. (11) and (22), we get

I mp



It

n0

KAU s [ 1  exp{  ( tt  tth )}]



n0  n  0 KAU s [ 1  exp{  ( tt  tth )}] S0 … (29)

where

KAU s [ 1  exp{   ( tt  tth )}]



 S0

Since the ML after the transit time tt, occurs due to the relaxation of blocked cracks during the generation of cracks by the moving shock waves, Imp should be a fraction f of It and therefore, we can write

I mp fI t

… (30)

n0 S0

…(31)

where f 

If f decreases exponentially with the shock pressure P, Eq. (30) can be written as

I mp It

 f 0 exp(  P)

…(32)

where κ and f0 are constants, and f=f0exp(-κP).

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It is evident from Eq. (32) that Imp/It should decrease exponentially with increasing shock pressure P. (xi) Determination of shock-wave velocity and shock pressure The transit time tt is the time at which the shock wave disappears. If T is the thickness of the target, then the shock-wave velocity Us can be expressed as Us 

T tt

…(33)

It has been shown that the shock pressure P is given by [1]

P  U p U s

...(34)

where ρ is the density of target material and Up is the velocity of projectile. Thus, using Eqs. (33) and (34) the shock-wave velocity Us and the shock pressure P can be determined. (xii)

ML spectra Brannon et al. [16] have reported that the radiation spectrum of quartz crystals

appears to be band-like rather than a black body or gray body as is expected for thermal radiation. In fact, the crystalline X-cut quartz has emission peaks near 600 nm with a minimum in output near 500 nm, and another maximum at or below 400 nm. A change in the 400 nm emission with time can be understood on the basis of wave interaction times. Brannon et al. [16] have studied the ML spectrum for X-cut quartz and they have obtained the emission bands around 400 and 600 nm. The band at 400-nm band has also been reported previously in photoluminescence [32], cathodoluminescence [33, 34], mechanoluminescence [35], X-rayexcited luminescence [36], and in thermoluminescence [37]. The 600-nm band has been reported in X-ray-excited luminescence [36], cathodoluminescence [33,34] and , in one case in photoluminescence[32], but in another study it was not observed in photoluminescence[35]. On 13

the basis of these observations, it is believed that the same emission centres are excited by shock waves as by the other means of above mentioned excitation. The band peak near 400 nm has been associated with an E’ centre [32,33]. Sigel [38] has given the following model of an E’ centre: the principal electron trap in a dangling sp3 orbital and the principal hole trap in the nonbridging p orbital of a nonbridging oxygen atom. The blue emission results when E’ centres are annihilated. The centre associated with the 660-nm has not been identified. Gee [39] has suggested that this emission arises from water impurity in SiO2.

4. Correlation between experimental and mathematical results Brannon [16] used a single-stage propellant gun to generate shockwaves in the specimen studied. The projectiles 89 mm in diameter and weighing 1.3 to 1.4 kg were propelled to velocities in the range of 0.6-2.4 km/s. Disks of X-cut crystalline quartz specimen were mounted in aluminium target plates. Impactor dimension was nearly 88 mm in diameter and 9.5 mm thick. Target diameter was nearly 50.8 mm and its thickness was 12.69 mm. The light generated by the target was observed from the side opposite the impact surface having 25-mm aperture. For the measurement of ML, 5 dichromatic beam splitters, 5 photomultiplier tubes, bandpass filters, and fast framing camera were used. Fig.1 shows 600-nm radiance for different shock pressures [16]. It is seen that, when a projectile propelled to velocities in the range of 0.6-2.4 km/s makes impact on the X-cut quartz target, then after a threshold time tth, where the shock pressure attains a threshold pressure Pth for the ML emission, initially the ML intensity increases linearly with time, then it attains a value It, at the transit time tt where the projectile stops, and subsequently the ML intensity starts decreasing with time. At the transit time tt, the shock pressure relaxes and then the cracks which

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were blocked by barriers or obstacles start moving. Thus, after tt, again the charged surfaces are created and the ML appears whose intensity increases with time, attains a value Imp at time tmp, and later on the ML intensity decreases and finally disappears. The linear increase of ML intensity is in accord with Eq. (9) and the attainment of a fixed intensity at t t is supported by Eq.(11). One feature which is evident in all of the data is the burst in radiance at the end of the pulse. The curves shown in figure 1 for different pressures have two such bursts. Fig.2 shows the semilog plot of ML intensity versus (t-tt) and semilog plot of ML intensity versus (t-tmp). It is seen that both the plots of straight lines with negative slopes. The values of decay times estimated from the inverse of slopes are shown in Table 1. The decay times are nearly the same for both the plots. This result indicates that both the ML in the compression region before tt and ML in the post transit region appear due to the creation of new surfaces. Fig. 3 shows the spectral data from X-cut quartz at different times during shock transit. The result shows that the ML spectra changes slightly with different times during shock transit. Fig.4 also shows the ML spectra of X-cut quartz at different times during shock transit. It is evident that there is a slight change in the ML spectra with different times during shock transit. Fig. 5 depicts the shock pressure dependence of Imp/It for X-cut quartz crystals. It is seen from Fig. 5 that the ratio Imp/It decreases with increasing value of the shock pressure. This finding follows Eq.(32). It seems that comparatively less area of newly created surfaces produced during the relaxation of shock pressure. This fact indicates that the decreasing size of fractured crystallites at high pressure increases the barrier for blocking the cracks because of the increase in the hardness of the crystals with increasing shock pressure.

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Fig.6 shows the shock pressure dependence of the radiance from X-cut quartz crystals. It is seen that initially the ML intensity increases with shock pressure, but between 6 and 8 GPa, the ML intensity decreases because of the phase-change in the quartz crystals. After 8 GPa, the ML intensity increases again with the increasing value of shock pressure. This result follows Eq.(27) for low value of the shock pressure. Fig.7 shows the shock pressure dependence of the transit time and shock velocity. It is seen that whereas, the transit time decreases with increasing value of the shock pressure, the shock velocity increases with increasing value of the shock pressure. Fig. 8 shows that the value of shock pressure P (experimental) increases with increasing value of the impact velocity of the projectile. The values of shock pressure P (theoretical) determined using Eq. (34) ( P  U p Us ) [1] for different values of the impact velocity are also shown in Fig. 8. The density ρ of quartz crystal is taken as 2.65 g/cm3. It is evident from Fig. 8 that the theoretical values are close to the experimental values. Initially, the ML intensity increases with the shock pressure because of the creation of more surfaces; however, for higher values of the shock pressure, the ML intensity tends to attain a saturation value because of the hardening of the crystals due to the creation of small crystallites in which the creation of new surfaces becomes difficult. The ML emission in the postcompression region takes place due to the movement of blocked cracks in the compression region when the pressure is relaxed. The ratio between Imp and It decreases with increasing pressure because more defects produced at high pressure generates higher barrier for the relaxation of blocked cracks under compression. Thus, a good agreement is found between the theoretical and experimental results.

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5. Conclusions Conclusively, it may be said that, when a projectile moving with velocities in the range 0.5 – 2.5 km/s makes impact on the target, then the shock waves travelling at a velocity on the order of 10 km/s produces intense mechanoluminescence (ML) pulse of microsecond duration, both in the compression and post-compression regions. Expressions explored for the characteristics of shock-induced ML are able to explain satisfactorily the experimental results. Shock-wave velocity, shock pressure, transit time, lifetime of electrons in the conduction band, etc. can be determined from the measurement of shock-induced ML. Thus, the shock-induced ML provides an important optical technique for the studies of materials under high pressure.

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[22] A.L. Kholkin, N.A. Pertsev, and A.V. Goltsev, Piezoelectricity and Crystal Symmetry(Chapter II): in Piezoelectric and Acoustic Materials for Tranducer Applications, A Safari and E K Akdogan (Eds.), Springer, New York, USA, pp. 17-38, (2008). [23] A. Ballato, Basic Material Quartz and Related Innovations (Chapter II): in Piezoelectricity Evolution and future of a technology, W Heywang, K Lubitz and W Wersing ( Eds.), Springer, New York, USA, pp. 9-33, 2008. [24]P. Heyligera, H. Ledbetter, S. Kim, J. Acoust. Soc. Am. 114, (2003), 644 99.45 GPa. [25] H. Kimizuka, S. Ogata, J. Li, Y. Shibutani, Phy. Rev.B 75, (2007) 054109. [26] B. P.Chandra, Mechanoluminescence, in Luminescence of Solids (Ed. Dr.Vij), New York: Plenum Press, 1998:361–89. [27] V.K. Chandra, B.P. Chandra, P. Jha, J. Lumin. 135 (2013) 139-153. [28] B.P. Chandra, K. K. Srivastava, J. Phys. Chem. Sol. 39 (1978) 939–940. [29] B.P. Chandra, Nuclear Tracks 10 (1985) 225-241. [30] J. Kalinowski, J. Phys. D: Appl. Phys. 32 (1999) R179. [31] G. A. Lyzenga, T.J. Ahrens, and A.C. Mitchell, J. Geophysical Research, 88 (1983)2431. [32] C M Gee and M Kastner, J. Non-Cryst. Solids 35(1980) 927. [33] J P Mitchell and D G Denure, Solid-State Electron. 16 (1973)825. [34] S W McKnight, “Electron-Beam-Induced Luminescence in SiO2,” in Proceedings of the International Topical Conference on the Physics of MOS, Insulators, North Carolina State University, Raleigh, NC, June 18-20, 1980, edited by G Lucovsky, S T Pantelides and F R Galeener (Pergamon, New York) p. 137. [35] J I Zink, W Beese, J W Schindler and A J Smiel, Appl. Phys. Lett. 40 (1982)110. [36] M J Marrone, Appl. Phys. Lett. 38 (1981)115.

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Figure Captions Fig. 1 Radiance at 600 nm for different shock pressures of X-cut quartz crystals disks of about 9.5 mm thick and 88 mm diameter, which were impacted with either 6061-T6 aluminium or tungsten carbide (WC) impactor. Projectiles 89 mm in diameter and weighing 1.3 to 1.4 kg were propelled to velocities 0.6-2.4 km/s (after Branon et al. ref.[16]). Fig..2 Semilog plot of ML intensity (Id1-Ir2) versus (t-tt), and semilog plot of ML intensity Id2 versus (t-tmp) X-cut quartz crystals. Fig. 3 Spectral radiance for X-cut quartz at 11.4 GPa (after Branon et al. ref.[16]). Fig.4 Spectral data from X-cut quartz at different times during shock transit (after Branon et al. ref.[16]). Fig.5 Shock pressure dependence of the ratio Imp/Itt for X-cut quartz crystals. Fig. 6 Shock pressure dependence of the radiance of X-cut quartz crystals (after Branon et al. ref.[16]) . Fig.7 Dependence of transit time and shock velocity on shock pressure. Fig.8 Dependence of shock pressure (experimental) and shock pressure (theoretical) on the projectile velocity.

20

Fig. 1

21

Fig. 2

22

Fig. 3

23

Fig. 4

24

Fig. 5

25

Fig. 6

26

Fig. 7

27

Fig.8

Table 1: Values of β, ξ, τ1 and τ2 for different values of shock pressure S

Pressure

β (μs-1)

τe (μs)

β (μs-1)

τe (μs)

No.

( GPa)

determined in

determined in

determined in

determined in

compressed

compressed

uncompressed

uncompressed

region

region

region

region

1.

7.8

3.190

0.313

3.289

0.304

2.

11.7

4.280

0.234

3.091

0.324

3.

14.5

4.140

0.242

5.014

0.199

28