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Investigation on the Thermal Expansion and Theoretical Densityof 1,3,5-Trinitro-1,3,5-Triazacyclohexane

Jie Sun,a Xiaoyan Shu,a Yu Liu,a Haobin Zhang,a Xiaofeng Liu,a Yan Jiang,a Bin Kang,*a Chao Xue,b Gongbao Songb

a Institute of Chemical Materials, China Academy Engineering Physics, Mianyang 621900, Sichuan, P. R. Chinae-mail: zhuoshisun@sohu.com; zhhb1987@yahoo.cn

b School of Materials Science and Engineering, Southwest University of Science and Technology, Mianyang 621010,Sichuan, P. R. China

Received: March 1, 2010; revised version: July 1, 2010

DOI: 10.1002/prep.201000026

Abstract

The CTE and the theoretical density are important propertiesfor energetic materials. To obtain the CTE and the theoreticaldensity of 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX), XRD,and Rietveld refinement are employed to estimate the dimen-sional changes, within the temperature range from 30 to 170 8C.The CTE of a, b, c axis and volume are obtained as 3.07�10�5 K�1, 8.28� 10�5 K�1, 9.19�10�5 K�1, and 20.7�10�5 K�1, re-spectively. Calculated from the refined cell parameters, the theo-retical density at the given temperature can be obtained. Thetheoretical density at 20 8C (1.7994 g cm�3) is in close match withthe RDX single-crystal density (1.7990 g cm�3) measured by den-sity gradient method. It is suggested that the CTE measured byXRD could perfectly meet with the thermal expansion of RDX.

Keywords: Coefficient of Thermal Expansion, RDX, RietveldRefinement, Theoretical Density

1 Introduction

As we know, energetic materials usually expand with in-creasing temperature, and this property of thermal expan-sion would be a crucial factor in application. It would in-fluence the molding process, lead to deformation of con-tainers, or even make excursion in rigorous application. Ifthe coefficients of thermal expansion (CTE) of explosivecrystals can be obtained, there will be some reference tosimulation of mechanical properties, loading structuredesign, and environmental adaptation of energetic materi-als. The theoretical density of explosive is also an impor-tant parameter for formulation design and crystal qualityvaluation [1]. What�s more, based on the theoretical den-sity, the detonation velocity, detonation pressure, andvoid ratio can be precisely evaluated.

So far, much effort has been achieved in the field ofthermal expansion. However, these researches almost fo-cused on inorganic materials [2–3], while the energeticmaterials were seldom studied. The current methods forCTE measurement include expansion gauge, X-raysingle-crystal diffraction and X-ray powder diffraction(XRD), etc. Making use of expansion gauge, the testedCTE of many explosives, such as HMX and TATB, arebased on slender cylinders [4–7], which cannot displaythe thermal expansion of explosive crystals completely.Kolb and Rizzo [8], Evers et al. [9] researched the CTEof TATB and FOX-7 by means of single-crystal diffrac-tion, respectively. There are also some reports that em-ployed powder diffraction to determine the CTE ofHMX [10–12] and TATB [13], of which the accuracy andreliability have been developed by our team [10,13]. Asto the theoretical density of RDX, the data in references[14,15, 16], are usually inconsistent while the value of1.806 g cm�3 is commonly accepted. So, there is still along way to go to study the thermal expansion and theo-retical density of energetic materials.

1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) is consid-ered to be the most important dynamite, and it has beenwidely studied on its properties and performance [17–22].However, the thermal expansion behavior of RDX crys-tals has been neglected more or less. There are reportsabout the calculated results from Agrawal et al. [23,24],measured data based on the slender cylinders [6], and theresults by means of thermomechanical analyzer of singlecrystals [25], but not the thermal expansion of explosivecrystals making use of XRD. In order to enhance thesafety, stability, and dependability of armaments, the in-vestigation on thermal expansion of RDX is very impor-tant. In this paper, XRD and Rietveld refinement were

Propellants Explos. Pyrotech. 2011, 36, 341 – 346 � 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 341

applied to investigate the thermal expansion propertiesand theoretical density of RDX. For the reliability of thetheoretical density and the refined results, the density ofan RDX single-crystal was measured by means of densitygradient method and was compared with the theoreticalone.

2 Materials and Methods

2.1 Materials

The RDX used for XRD measurement was recrystallizedin acetone with a purity of 99.9%. The average particlesize was around 20 mm with the central 80% being be-tween 10 and 30 mm.

To get reliable information in density measurement, awell developed RDX single crystal was prepared, withthe particle size about 3 mm.

2.2 XRD Measurements

X-ray diffraction data was collected through a Bruker D8Advance X-ray diffractometer by using Cu Ka radiationwithout any monochromator. A TTK 450 temperaturechamber was used to precisely control the temperatureduring experiment. The X-ray tube operating conditionswere 40 kV and 40 mA and a Vantec-1 detector wasadopted. The sample was scanned from 10 to 608 in 2q,with an increment of 0.028 and a scanspeed of 0.2 s perstep. A series of XRD analyses were undertaken from 30to 170 8C in steps of 20 8C.

2.3 Density Measurements

To confirm the refined results, the density of the RDXcrystal and the coefficient of density change are measuredby means of density gradient method [26]. The principleof density gradient method was illustrated in Figure 1.

The column filled with gradient liquid was immersed ina water bath, through which the temperature was con-trolled and altered. The gradient was achieved by aslowly mixing of a high-density aqueous ZnBr2 solution(1.8523 g cm�3) with a low-density one (1.7778 g cm�3)under magnetic stirring, before feeding liquid into the

column. After stabilizing the equipment for about half anhour at the fixed temperature (20 8C), the calibratedquartzose floats were delivered into the column for equi-librium. Then the density curve for the column could bedepicted, which was generated from the densities of floatsand their positions in the column after achieving equilib-rium (shown in Figure 2).

In the determination of density gradient method, floatsare a very important medium for the transfer of data, sothe character and density accuracy of the floats would di-rectly influence the results. The CTE of quartzose floatsis less than that of vitreous floats by one order of magni-tude. So six quartzose floats, with the density of 1.7818,1.7863, 1.7928, 1.7996, 1.8042, and 1.8106 g cm�3 were ap-plied for the wide temperature range. The quartzosefloats had been certificated by H & D Fitzgerald Ltd, UK[27].

Before adding sample, the RDX single-crystal waswetted by light-density liquid to avoid importing air bub-bles into the column. We let the sample sink and thenkept it for at least 1 h to reach equilibrium. Later, the po-sition of RDX particle was counted for the density calcu-lation, which was operated within the density curve thathad been obtained in previous work. Then the tempera-ture was turned to the next point for another measure-ment. The temperature order was set as 10, 15, 20, 25, 30,35, and 40 8C.

3 Results and Discussion

3.1 Coefficient of Thermal Expansion

The XRD patterns of RDX during heating from 30 to170 8C with a rate of 0.1 K s�1 was measured in steps of20 8C. Two of them (30 and 170 8C) are presented inFigure 3. From the X-ray diffraction patterns of RDX, noother changes could be observed except the shift of posi-tion in Bragg reflections to lower 2q angles. Besides, thisexcursion displays an augment with the gradually climbedtemperatures. It could be indicated that no phase trans-Figure 1. The sketch graph of density gradient column.

Figure 2. The curve of density versus height for the standarddensity floats.

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formation but expansion of the lattice would take placewithin the temperature range [28]. The crystal phase isconfirmed to be a-RDX, since the peak positions in theobtained XRD patterns are consistent with file 44–1618in [14], without the existence of metastable phase of b-RDX, which also exists at ambient pressure and tempera-ture [29].

There are many references in literature reporting thelattice parameters and theoretical density of RDX, butthe results are inconsistent with each other, just as listedin Table 1. The axis orientation chosen for this study is

such that the lattice parameters are a=1.3182 nm, b=1.1574 nm, and c=1.0709 nm, an orientation used byChoi and Prince [15] in their article on the crystallograph-ic data of RDX. Based on the information obtained fromthe given XRD patterns, the Rietveld method is em-ployed to get the refined lattice parameters of RDX cor-responding to a certain temperature point. All the crystal-lographic information is summarized in Table 2.

Linear fitting for a series of refined lattice parametersas a function of temperature has been done, as shown inFigure 4. During the heating and cooling process, littledifference of lattice parameters existed, so just the resultsduring heating process are linear fitted.

A clear increase in the parameters of a-, b-, and c-axiswith temperature could distinctly be observed from thesegiven figures, and the parameters tend to increase withgood correlation coefficients (R). Since all the values ofR are bigger than 0.998, it can be considered that thechange of lattice parameters with temperature variation islinear and the CTE are invariable during this temperaturerange.

On basis of the results depicted before, it is easy to getknown of the linear CTE by mathematical calculation ofa-, b-, and c-axis, which is about 3.07� 10�5 K�1, 8.28 �10�5 K�1, and 9.19�10�5 K�1, respectively. Evidently, theb- and c-axis exhibit approximately equal thermal expan-sion, but the thermal expansion of a-axis is about 1/3 ofthat along b- and c-axis, and this may be attributes to thestronger intermolecular electrostatic forces in the direc-

Figure 3. XRD curves of RDX at elevated temperature.

Table 1. Lattice parameters of RDX in references.

No. a b c Volume Density T Reference(nm) (nm) (nm) (nm3) (g·cm�3) (K)

1 1.3182 1.1574 1.0709 1.63386 1.806 Ambient [14, 15]2a) 1.3140 1.1420 1.0586 1.55848 1.893 90 [16]3 1.3192 1.1594 1.0714 1.63840 1.801 Ambient [14]4 1.3202 1.1601 1.0717 1.64138 1.798 Ambient [14]

a)The crystalographic axes have been adjusted.

Table 2. Lattice parameters of RDX refined from XRD data.

T a b c Volume Density(8C) (nm) (nm) (nm) (nm3) (g·cm�3)

30 1.31997 1.16089 1.07244 1.64335 1.795650 1.32088 1.16292 1.07426 1.65014 1.788270 1.32157 1.16484 1.07599 1.65640 1.781490 1.32230 1.16670 1.07779 1.66274 1.7747

110 1.32314 1.16868 1.07978 1.66970 1.7673130 1.32380 1.17045 1.08166 1.67598 1.7606150 1.32499 1.17263 1.08414 1.68445 1.7518170 1.32567 1.17428 1.08624 1.69096 1.7450150 1.32486 1.17258 1.08409 1.68414 1.7521130 1.32387 1.17050 1.08171 1.67621 1.7604110 1.32312 1.16872 1.07983 1.66981 1.767190 1.32215 1.16666 1.07778 1.66249 1.774970 1.32162 1.16496 1.07623 1.65700 1.780850 1.32058 1.16292 1.07430 1.64983 1.788530 1.31964 1.16095 1.07255 1.64318 1.7958

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Investigation on the Thermal Expansion and Theoretical Density of 1,3,5-Trinitro-1,3,5-Triazacyclohexane

tion of a-axis. So, an anisotropic thermal expansion ofRDX is revealed here. The change of volume has beenconcerned as well. The CTE for volume is about 2.07 �10�4 K�1, with a 2.5 % change from 30 to 170 8C. All ofthe data are detailed in Table 3.

It should be concerned that the CTE of the lattice pa-rameters didn�t agree well with the results given by Cady[25]. According to the results of Cady, the CTEs arerising with temperature, with different changing rates.During the temperature range from 30 to 135 8C, the co-efficients of CTEs changing with temperature are 1.1 �10�7 K�2, 0.38 �10�7 K�2, and 3.1� 10�7 K�2, for a-, b-, andc-axis, respectively, after adjusting the choice of axes toidenticalness. But our results indicate that the CTE forRDX lattice parameters are invariable, which can also beapproved by comparing the density of refined data withmeasured ones. The difference may come from differentexperimental methods, and the imperfect of single crystalCady used in the experiment, such as liquid inclusion,cracks, dislocation, and so on, may also take an effect onthe results.

3.2 Density

With the obtained density from Rietveld refinement, therelation of density, and temperature could be expressedby the following equation:

1 ¼ 1:8066�3:607� 10�4*T ð1Þ

It means that a shift of 0.001 g cm�3 in density could beinduced by every changed 3 K. Through the extrapolationof linear fitting, the theoretical density is obtained as1.7994 g cm�3 at 20 8C.

The density of the RDX single crystal is also measuredby density gradient method. Due to the influence of envi-ronmental temperature, a departure from the preconcert-ed temperature is observed during the experiment. Theactually measured density changing with temperature forRDX single crystal is shown in Figure 5. A regular de-crease in density as temperature rised could be observedby linear fitting of the experimental data.

From the given data, it could be found that the densityof the single crystal of RDX at 20 8C is 1.7990 g cm�3,while the theoretical one is 1.7994 g cm�3. The odds may

Figure 4. Linear fitting for lattice parameters of a-, b-, and c-axis and volume of RDX during the heating process.

Table 3. Linear CTE a, volume, and density change.

Temperature aaa) ab ac aV Volume Change

(K) (10�5 K�1) (10�5 K�1) (10�5 K�1) (10�5 K�1) (%)

In this work 303–443 3.07 8.28 9.19 20.7 2.5Ref. [25]b) 295 2.61 8.68 7.86 19.1

a) a means CTE aa, ab, ac and av mean the CTEs of a-, b-, c-axis and the volume, respectively. b) The crystalographica axes have beenadjusted.

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be induced by the inclusion of residual solution duringthe course of developing the single crystal, however, thedifference is just 0.02 %. Comparing with our results, thedensities given in Refs. [14,15] are a little higher, whichmay result from several factors, such as different temper-ature controlling, immature testing instruments, and soft-ware limiting in the earlier period of time.

It could be noted that the coefficient of density change(given in Figure 5), �3.596�10�4 g cm�3 K�1, is close to thatfrom Rietveld refinement �3.607�10�4 g cm�3 K�1, with anerror below 0.3%. The slight deviation in density of refinedresults and measured one as well as their equivalent changecoefficient confirm strongly that the refined results aboutthe thermal expansion of RDX are reasonable and credible.

The density of RDX decreased toward temperaturewith the coefficient of 3.607 �10�4 g cm�3 K�1, which ishigher than that of HMX [10], though they have thesame element composition and always coexist with eachother. The difference may be caused by the lower stackedstate in RDX, which resulted in a weaker electrostaticforce. So RDX tends to express a greater expansion thanHMX when heated.

4 Conclusion

By means of XRD and Rietveld refinement, the coeffi-cient of thermal expansion and the theoretical density ofRDX crystal have been obtained. The theoretical densityof RDX from XRD and Rietveld refinement agrees wellwith the measured one from density gradient method,which indicates that the results are reasonable and credi-ble. The results obtained might provide guidance for ap-plication of RDX.

Acknowledgement

This work is supported by the National Science Foundation,China (no. 10979037).

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