DLIN-B 75-0292

The isothermal linear and volume compression of pentaerythritol tetranitrate (PETN) to 10 GPa (100 kbar) and the calculated shock compression

Bart Olinger, P. M. Halleck, and Howard H. Cady

Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87544 (Received 3 February 1975)

The isothermal linear and volume compressions of the explosive pentaerythrito\ tetranitrate (PETN) were measured to 10 GPa using a high pressure x-ray diffraction technique. The fits to the data are alao = 1- 2.052 x l0- 2p + 2.230 X IO- 3p 2 - 1.041 X IO -<p 3, and clco = 1-2.832 X I0- 2p + 3.295 X IO- 3p 2 - 1.458 X IO- ·p 3, for P < 10 GPa, and u " = 2.16 + 3.007 uP' - 0.682 u;" for up, < 0.95 km/s and u" = 2.76 + 1.71 up, for up, > 0.95 km/s, where u., = [PVo/(1- V/ VO)]I /l , uP' = [P V o(1 - V IV J]"2, and Po = 1/Vo = 1.774 glcm3. The shock compression Hugoniot of PETN calculated from the isothermal compression fit is u , = 2.24 + 2.95 u p - 0.605 u~, for up < 1.00 km/s and Us = 2.81 + 1.75 up for up> 1.00 km/s, where u, is the shock velocity and up is the l particle of mass velocity behind the shock wave. The isothermal compression fit and the Hugoniot are initially quadratic because of the rapid change in the strength of repulsive forces between the PETN molecules during initial compression.

The shock compression of pentaerythritol tetranitrate (PETN) is an important factor in understanding the in­itiation of this explosive. PETN, C(CH20N02)., is a complex molecular organic solid whose symmetry and cell size (2 molecules per tetragonal unit cell)l make it ideal for determining its isothermal compression using a recently developed high pressure x-ray diffraction technique. 2 From the isothermal compreSSion, the shock compression can be readily calculated.

The experimental technique can be described briefly as follows. PreCipitated PETN powder, NaF powder, and a mixture of 4: 1 methanol-ethanol are placed in a 0.3 mm diam hole drilled through the center of a 0.3 mm thick, 3.0 mm diam beryllium disk. The effects of localized nonhydrostatic stresses in the sample mix­ture and of pressure gradients across the sample re­gion are eliminated with the addition of the alcohol mix­ture which remains liquid to 10 GPas (1 GPa= 10kbar, the International System of Units is used throughout this report). The disk is pressed between two tungsten­carbide anvils, one driven by a hydraulic ram. A col-17mat..ect..~.x -.ay be~'\-n is passed through the sample perpendicular to the direction of applied stress and the subsequent diffraction pattern recorded on a film in a 114.6 mm diam powder camera surrounding the sam­pIe. Typical exposure times are from 8 to 16 h.

Diffraction patterns for the exposures taken at high pressures exhibited the 020, 021, 121, 220, 012, 130, 031, 131, 122, and 222 diffraction lines of PETN and the 200, 220, and 222 diffraction lines of NaF. Correc­tions for the sample position and self-absorption were made for the high pressure patterns on a line-by-line basis. These corrections were found by comparing three initial diffraction patterns of the sample taken at ambient conditions in their high pressure configuration with the standard patterns.. The standards for the cor­rections were derived from the NaF unit cell parameter (0.43342 nm) determined by Swanson and Tatge· and precipitated PETN unit cell parameters (a = O. 9386 ±0.0003nm, c =0. 6715:1:0.0002nm, Po= 1. 774 g/cmS)

determined here using filtered CuK radiation, a 114.6

4480 The Journal of Chemical Physics, Vol. 62, No. 11 , 1 June 1975

nm powder camera and a lattice constant refinement program. The pressure deduced from the volume com­pression of NaF are listed elsewhere. 5

Because the heats of fusion of PETN samples pre­pared in different manners differ significantly,6 the unit cell parameters of ground single crystal PETN were measured to see if they also differed from those of pre­cipitated PETN. The parameters (a=0.9383:t:0.0004 nm, c=0.6711:t:0.0003 nm) are nearly identical to those of the rapidly precipitated PETN indicating that bonding is the same in the two and that the impurity content of the two is the same Or negligible. Consequently, the inter- and intramolecular compression of rapidly pre­cipitated PETN and single crystal PETN will be the same.

The cell edge compressions and the consequent vol­ume compressions are listed in Table I with the volume compressions of NaF and the deduced pressures. The accompanying standard deviations of the data follow them in parentheses. In Figs. 1 and 2 are plotted the cell edge compression and volume compression data.

In the present study we will not examine in detail the inter- or intramolecular compression of PETN. We will, instead, give a description of its isothermal and shock compressions. It is obviOUS, however, from Fig. 1 that the compression along the c axis, or (001) di­rection, is greater than along the a axis, or perpendicu­lar to the (001) direction. The quantitative descriptions of the axes' compressions as a function of pressure are

a/a 0 = 1 - 2. 052x 10-2p+ 2. 230x 10-3p2 -1. 041x 1O-~p3 (la)

c/eo= 1 - 2. 832x 1O-2p+ 3. 295x 10-3 p2 -1.458X 10-·ps

for P < 10 GPa. (lb)

This is in qualitative agreement with the linear thermal expansions measured by Cady7 [ac=9.05 x I0-5/K, a4

= 7 • 07 x 10-5/ K, therefore with change in temperature at 298 K, (t.c/co)/(~/ao) = 1. 28].

Pastines has recently discussed the mechanism for

Copyright © 1975 American I nstitute of Physics

Olinger, Halleck, and Cady: Compression of pentaerythritol tetranitrate 4481

TABLE 1. Linear and volume compressions of PETN and the simultaneous compressions of NaF with its correlated pressures.

P ET Na PETN" PET'" NaFd Pressure' a/ ao clco VI Vo VI Vo GPa

.0.9828 (6) .0 . 977.0 (11 ) .0 . 9437 (23) .0. 986.0 (26) .0 . 68 (.0 .15)

.0. 9794 (5) .0 . 9675 (11 ) .0.928.0 (21) .0 . 9825 (2.0) .0 . 86 (.0 .11 )

.0 .9754 (5) .0 . 9636 (8) .0 . 9168 (18) .0 . 9749 (29) 1. 28 (.0.11)

.0. 971.0 (7) .0.9598 (13) .0 . 9.049 (27) .0 . 9675 (13) 1. 71 (G • .06)

.0. 9596 (9) .0.9517 (16) .0 . 8763 (34) .0 . 9588 (4) 2. 25 (G • .03)

.0.9565 (8) .0 . 9393 (13) .0 . 8594 (29) .0 . 9483 (2 7) 2 . 9.0 (.0. 15)

.0. 9537 (6) .0 . 9391 (1 G) .0.8524 (22) .0 . 94.04 (22) 3.42 (.0 . 12)

.0.9514 (3) .0 . 9375 (5) .0.8486 (11 ) .0.9388 (33) 3 . 53 (.0 . 22) G. 9~10 (7) .0 . 9378 (12) .0.8481 (26) .0 . 9386 (8) 3 . 55 (G • .05) .0.9497 (6) .0.9324 (9) .0 . 841.0 (21 ) .0 .9372 (4) 3.65 (G • .02) .0 . 9488 (7) .0 . 93.06 (14) .0 . 8378 (28) .0.9328 (6) 3.95 (G • .04) .0.9446 (1.0) .0 . 9263 (13) .0 . 8265 (33) .0 . 92.01 (2 ) 4.9.0 (G • .02) .0 . 9411 (3) .0 . 923.0 (5) .0 . 81 75 (11 ) .0 . 919 .0 (21) 4 . 98 (.0.16) .0.94.07 (4) .0.9226 (6) .0 . 8163 (14) .0 . 9187 (20) 5. 0.0 (0 .1 7) .0 . 9385 (9) 0. 9208 (15) .0 . 811 .0 (33) .0 . 91.03 (17) 5.64 (0 . 15) .0.9372 (9) .0 . 9217 (14) .0.8.096 (32) .0 . 9.087 (8) 5.76 (G • .07) .0 . 9359 (6) .0 . 9181 (9) .0 . 8.042 (2 1) .0.9.083 (1 .0) 5.8.0 (0 • .08) .0 . 9317 (7) 0. 9145 (9) .0 . 7938 (23) .0 . 8975 (3) 6 .73 (0 . 01) .0.9286 (5) 0. 9112 (9) .0. 7856 (19) 0. 8941 (15) 7 . .02 (.0 . 12) .0 . 93.01 (9) .0 . 9147 (13) .0.7913 (31) .0 . 8938 (12) 7 • .os' (.0 .1 3)

.0.9287 (6) .0 . 9123 (6) .0 . 7864 (18) .0 . 8923 (28) 7. 17 (.0.25)

.0 . 9267 (8) .0 . 91.04 (16) 0. 7818 (32) .0 . 8894 (32) 7.45 (.0 . 27)

.0.9264 (5) .0 . 9135 (1 .0) .0 . 784 .0 (20) 0.8878 (1) 7.6.0 (G . GO 0 . 9264 (6) .0 . 9.083 (11 ) .0 . 7796 (23) 0.8872 (6) 7 . 65 (G • .os) .0 . 922.0 (8) .0 . 9.093 (13) .0 . 773.0 (29) .0 . 8823 (2) . 11 (G. GO .0 . 9236 (6) .0 . 9076 (11) .0 .7742 (23) .0 . 88.02 (5) 8. 32 (G • .04) .0 . 92.05 (6) .0 . 9.053 (12) .0 . 7671 (24) .0 . 8795 (3.0) 8 . 4.0 (.0 . 28) 0.9205 (8) .0 . 9.024 (15) . .0.7647 (31) .0 . 8732 (3.0) 9 • .04 (.0 . 27) .0. 919.0 (6) 0. 9.010 (11) .0 . 7609 (23) .0.8718 (35) 9.16 (.0.3.0) .0 . 9135 (8) .0.9.018 (13) .0 . 7525 (29) 0 . 8628 (11) 1.0. 12 (.0 .1 4) 0 . 9123 (7) .0 . 9.018 (1.0) .0.75.05 (24) O. 597 (3) 10.45 (G • .02)

--'The standard deviation x 104 given in parentheses. "The standard deviation given in parentheses.

the compression of organic explosives such as PETN in terms of changes in the type of repulsion forces during compression. At ambient conditions the covalently bonded molecules of PETN are bonded to one another by weak van der Waals attractions. 1 The initial compres­sion is almost entirely due to a reduction of intermolec­ular distances. At small intermolecular distances, strong van der Waals repulsions build up and become

10 .0

9.0 " .. ••• ••

8 .0 • 0/0 0 ••• I ,/ 7.0 ,. • 0 • •

Cl.. 6 .0 (9 ., ,

Q) 5 .0 /'. '. ~

::3 clco (/) 4 .0 • • (/) • ... .. . Q) ~

3.0 Cl.. • • 2.0 • •

• • • • 1.0 • • • •

0 .90 0.92 0.94 0 .96 0.98

FIG. 1. The data for the linear compression (xl xo) of tetrag­onal PETN.

10 .0

9.0 .. 8.0

., .,

7.0 I. e • (l.

t.? 6 .0 ., Q) 5.0 •• .... :::l (/)

4 .0 (/) • Q) ••• .... 0.. 3.0 •

2 .0

1.0

0 .76 0 .80 0 .84 0.88 0 .92 0 .96

VIVo

FIG. 2. The data for the volume compression, VIVo, of PETN (dotsl. Here they are compared with the initial slope of com­pression [the bulk modulus, AP/A(V/Vo») determined from PETN single crystal elastic constant data8 (8.3 GPal. The volume compression of Vasil 'ev et al. 7 is also shown (crosses).

comparable to the intramolecular repulsions along the covalent bonds. Thus initially the rate of change of compressibility should vary rapidly and gradually de­crease as all types of repulsive bonds become uniformly strong.

In Fig. 2 the volume compression data is compared with that measured by Vasil'ev et al. 9 and the initial slope of compression determined from elastic constant data for single crystal PETN. 10 The data agree well. The data of Vasil'ev et al. 9 show PETN to be slightly less . compressible than the present data. The initial bulk modulus determined from the elastic constant data is 8.3 GPa at zero pressure. At 10 GPa the bulk mod­ulus is 100 GPa (estimate from graph). This means the average pressure differential of the bulk modulus over the first 10 GPa of compression is 9, a high value in­dicative of a large change in the repulsive strength un..-_ dergone by PETN during compre-ision. - ...... _. -

A more sensitive means of examining the compres­sion of PETN is to transform the P, V data in Table I into two other parameters, [PVo/(l- V/VO)]1/2 and [PVo(l- V/VO)]1/2. Under shock compression condi­tions these parameters are the P, V expressions for the shock wave velocity, us, and the particle (or mass) ve­locity behind the shock wave, u,. For lack of better terms and for convenience we shall call the parameters the isothermal shock velocity, ust , and the isothermal particle velOCity, U,f, since they are derived from P, V conditions along the isothermal compression curve . The data of Table I is plotted in this form in Fig. 3, as is the data of Vasil'ev et al. 9

The data in the form of usf> U,t (Fig. 3) are inter­preted as follows. The value of the intercept for a fit to the data, Ct, at U,t = 0 km/s, is the value for the iso­thermal bulk sound speed in km/s. It can thus be re­lated to the isothermal bulk modulus at zero pressure

J. Chern. Phys., Vol. 62, No. 11, 1 June 1975

4482 Olinger, Halleck, and Cady: Compression of pentaerythritol tetranitrate

5 .0

4 .8

4.6

4.4

4 .2

4.0

~ 3.8 E

oX

N 3.6 / •

" / ::::::::' 3.4 /

~ +/ "- 32 ..,+/ > t/

I 3.0

tV - t?v "- +1 >0 2.8 +/ 0... +/

2.6 +/ • +1 2.4

/ I

2.2

2.0

0 .2 0.4 0 .6 0 .8 1.0 1.2

[PVo (I-VlVo)]"2(km/s)

FIG. 3. The present data (dots) and that of Vasil'ev et al. 7

(crosses) plotted in the form [PVo! (1 - V!Vol]1/2 and [PVo(l - V!Vo)]1/2. The isothermal bulk sound speed, 2.16 km! s, determined from elastic constant dataB is plotted as a diamond along the [PVo!(l- V/Vo)J1/2 axis. The solid line is the iso­thermal compression fit to the present data and the dashed line is the shock compression Hugoniot calculated from that fit.

Bto= PoC~ • (2)

From the initial slope St the pressure derivative of the bulk modulus at zero pressure can be calculated

(3)

Both ct and St have t subscripts to indicate isothermal conditions since similar terms are used to describe fits to sno~ t: mp:ession data.

Normally, the compression of metallic, co-valent, or ionic bonded solids can be described in terms of a simple linear equationll

ust =Ct +StuJJt • (4)

However, it is obvious from Fig. 3 that the data are not linear. Again, this is caused by the initial rapid compression of PETN with the closing of the weak in­termolecular van der Waals bonds. A more accurate description of the initial compression would be in terms of a quadratic equation

(5)

Unfortunately, as the data approaches zero pressure the (1 - V /Vo) component of ust and u# is dominated by the experimental uncertainty associated with V. Thus the intercept calculated from the data would have a large statistical error associated with it. Instead, we have chosen to force the quadratic fit through the isothermal

bulk sound speed calculated from the elastic constants.

Morris10 determined the adiabatic bulk sound speed to be 2. 24 km/ s. To transform this to its isothermal value we make use of the following thermodynamic equa­tion:

!!L c~ Cy =~=- •

Bs Cs Cp (6)

Here Ct and Cs are the isothermal and adiabatic sound speeds, and Cy and Cp are the heat capacities at con­stant volume and pressure. Cp for PETN at 298 K is 1.084 J/K. g.12 C" can be calculated from C~ using the following equation,

(7)

Here (lI" is the thermal expansion of PETN; Cady7 re­ports this to be 23. 195 X I0-li/Kat 298 K. By substitut­ing Morris' Cs for Ct into (7) we calculate an initial C". Then we recalculate using the Ct value from Eq. (6) found using the initial CJ C, value. After repeating this we find the values quickly converge, and that C" = 1. 009 J/K' g and ct = 2.16 km/s.

Using the calculated ch we find the quadratic fit to the ustJ U~t data in Fig. 3 to be

(8)

A compression calculated from such a quadratic fit cannot be extended much beyond the limits of the data. However, the data does appear to become linear above uJJt = O. 8 km/s, and the linear fit to those data is

ust=2.76+1.71uJJt. (9)

This is reasonable since all repulsion forces through­out the PETN should be uniform, and the compressed PETN should behave as a normal covalent solid under compression. The two fits can be smoothly connected at u# = O. 95 km/s; here their tangents are the same. The V, P plot in Fig. 2 can now be fit using expression (8) for U,t < 0.95 km/s and expression (9) for U~t >0.95 km/s, where

V/Vo=(ust -u#)/ust (10)

and

P=POUstU,t (11)

The quadratic fit for the Vasil' ev et al. 8 data is

Ust = 2. 367 + 2. 72u# - O. 336u~ • (12)

The bulk modulus is larger than that of Morris (9.9 GPa) compared to Morris' 10 8.3 GPa) and Vasil'ev et al. 's zero pressure, pressure differential of the bulk modulus is smaller (9.9 compared to our 11. 0). Both these slight differences could be due to the internal fric­tion of piston-cylinder apparatus of Vasil'ev et al., and the shear strength their PETN sample.

From the measured isothermal compression of PETN, an accurate shock compression of PETN can be calcu­lated barring any phase transition that may occur at elevated temperature. We begin by solving for the en­ergy change along the isothermal compression from the initial volume Vo to a volume at high pressure VL

J . Chem. Phys., Vol. 62, No. 11 , 1 June 1975

Olinger, Halleck, and Cady: Compression of pentaerythritol tetra nitrate 4483

The subscript t again refers to the isothermal com­pression curve. 'Y is the GrUneisen constant

'Y = o!" c~/ C~ •

(13)

(14)

From the values of O!", C~, and Cs we discussed earlier, we find 'Y = 1.07. The first assumptions we make are that CII and 'Y/V remain constant under pressure. 13

Though the values of these probably do vary since PETN has already been shown to behave differently from ma­terials for which these assumptions were originally made, such variations will not make much difference in the calculated Hugoniot. In turn, the energy change along the shock compression Hugoniot from Vo to the same VL iS 13 •

(15)

The subscript, h, refers to the Hugoniot. Finally, to complete the energy cycle [E~{Vo) = Et{Vo)], we must determine the energy difference between P~{VL) and pt{VL). We calculate this difference from the following thermodynamic expression,

(&E/ap),,=v/y • (16)

As stated earlier V /'Y is assumed to remain constant and have the same value as at ambient conditions, 0.53 cm3/g. Thus,

E/l{VL) -Et{VL)={V/Y)[P~{VL) -pt{VL)] • (17)

Combining Eqs. (13), (15), and (17), a solution for P~ as a function of Pt and VL can be found,

P~(VL) pt(VL)(V/y) + Iv) Pd~ - [T(Y/V)CY]{VL - Yo) • [tv y) - 2(VO - VL )]

(18)

The integral in Eq. (18) is solved by numerical integra­tion

where

V~= Vo(u.st~ -U~I')/U&fl'

and

(19)

(20)

(21)

An interval of 4 u" = 0.01 km/ s was found to be ade­quate.

The calculated values for P" and the corresponding values of VL were transformed to values for Us and u~

using [p~ VoI{l- VdVo)]1/2 and [P~Vo(l- VL/VO)]1/2. The plot of this calculated Hugoniot from the isothermal fits, Eqs. (8) and (9), appears also in Fig. 3. The corresponding quadratic and linear fits for this Hugoniot are

Us = 2. 24 + 2. 95u~ - o. 605u!, u~ < 1. 00 km/s, (22)

and

Us = 2. 81 + 1. 75u~, u~ > 1. 00 km/s • (23)

A preliminary linear fit to shock compression data on single crystal PETN for u~ values between 0.5 and 1. 5 km/sH is

us=2.87+1.69u~ • (24)

This agrees well with the calculated Hugoniot.

ACKNOWLEDGMENTS

We thank Joseph Fritz from the M-6 Group of the Los Alamos Scientific Laboratory for instructing us in the methods and theory of calculating Hugoniots from isothermal compressions. We also thank M. Ya. Vasil'ev for sending us a listing of his volume compres­sion data on PETN. The work was supported by the U. S. Atomic Energy Commission.

tAo D. Booth and F. J . Llewellyn, J. Chern. Soc. 1947, 837. 2p. M. Halleck and B. Olinger, Rev. Sci. rnstrum. 45, 1408

(1974), aG. J. Pi.ermarini, S. Block, and J. D. Barnett, J. Appl. Phys.

44, 5377 (1973). tH. E. Swanson and E. Tatge, Standard X-ray Diffraction

Powder Patterns (National Bureau of Standards, Washington, D. C., 1953), Circ. 539, Vol. I, p. 63.

5W• J. Carter, High Temp. -High Press, 5, 313 (1973). 6H. H. Cady, Report LA-4486-MS, Los Alamos Scientific

Laboratory, Los Alamos, NM 87544. 1H. H. Cady, J. Chem. Eng. Data 17, 369 (1972). 8D. J. Pastine, Proprietes PhYSiques Des Solides Sous Pres­

Sion, edited by D. Block, (Centre National de La Recherche Scientifique, Paris, 1970), p. 49; D. Pastine and R. R. Bernecker, J. Appl. Phys. 45, 44))8 (1974).

9M. Ya. Vasil'ev, D. B. Balashov, and L. N. Mokrousov, RUSB,

J. Phys. Chem. 34, 1159 (1960): M. Ya. Vasil'e~-rnstitute of Chemical PhysiCS, Moscow, U.S.S.R., 1974 (private com­munication).

tOC. E. Morris, Los Alamos Scientific Laboratory, Los Alamos, NM 87544, 1974 (private communication).

!tB. Olinger and P. M. Halleck, J. Chem. Phys. 62, 94 (1975). t2R. Rogers, Los Alamos Scientific Laboratory, Los Alamos,

NM 87544, 1974 (private communication). t3R. G. McQueen, S. P. Marsh, and J. N. Fritz, J. Geophys.

Res. 72, 4999 (1967). 14S. P. Marsh, Los Alamos Scientific Laboratory, Los Alamos,

NM 87544, 1974 (private communication).

J . Chern. Phys., Vol. 62, No 11, 1 June 1975