Thermoelastic equation of state of boron subphosphide B₁₂P₂
Compressibility of boron subphosphide B₁₂P₂ has been studied under quasi-hydrostatic conditions up to 26 GPa and 2600 K using laser-heated diamond anvil cell and angle-dispersive synchrotron X-ray diffraction. Вивчено стисливість субфосфіда бору B₁₂P₂ в квазігідростатичних умовах до 26 ГПа і 2600 К...
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Solozhenko, V.L. Cherednichenko, K.A. Kurakevych, O.O. 2019-10-22T17:32:24Z 2019-10-22T17:32:24Z 2017 Thermoelastic equation of state of boron subphosphide B₁₂P₂ / V.L. Solozhenko, K.A. Cherednichenko, O.O. Kurakevych // Сверхтвердые материалы. — 2017. — № 1. — С. 94-98. — Бібліогр.: 23 назв. — англ. 0203-3119 https://nasplib.isofts.kiev.ua/handle/123456789/160100 661.657/.636:539.58 Compressibility of boron subphosphide B₁₂P₂ has been studied under quasi-hydrostatic conditions up to 26 GPa and 2600 K using laser-heated diamond anvil cell and angle-dispersive synchrotron X-ray diffraction. Вивчено стисливість субфосфіда бору B₁₂P₂ в квазігідростатичних умовах до 26 ГПа і 2600 К в алмазних ковадлах з лазерним нагрівом методом дифракції синхротронного випромінювання. Изучена сжимаемость субфосфида бора B₁₂P₂ в квазигидростатических условиях до 26 ГПа и 2600 К в алмазных наковальнях с лазерным нагревом методом дифракции синхротронного излучения. The authors thank Dr. V. A. Mukhanov for the samples synthesis, Dr. Y. Le Godec for the DACs preparation, and Dr. Z. Konôpková (DESY) and Dr. L. Gigli (Elettra) for assistance in the synchrotron experiments. High-pressure experiments at DESY have been carried out during beam time allocated to the Projects DESYD-I-20090172 EC and DESY-D-I-20120021 EC and received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement No 226716. Experiments at Elettra have been performed during beam time allocated for the Proposal No 20160086. This work was financially supported by the Agence Nationale de la Recherche (grant ANR-2011-BS08-018) and European Union’s Horizon 2020 Research and Innovation Programme under Flintstone2020 project (grant agreement No 689279). en Інститут надтвердих матеріалів ім. В.М. Бакуля НАН України Сверхтвердые материалы Письма в редакцию Thermoelastic equation of state of boron subphosphide B₁₂P₂ Article published earlier |
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Thermoelastic equation of state of boron subphosphide B₁₂P₂ |
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Thermoelastic equation of state of boron subphosphide B₁₂P₂ Solozhenko, V.L. Cherednichenko, K.A. Kurakevych, O.O. Письма в редакцию |
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Thermoelastic equation of state of boron subphosphide B₁₂P₂ |
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Thermoelastic equation of state of boron subphosphide B₁₂P₂ |
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Thermoelastic equation of state of boron subphosphide B₁₂P₂ |
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Thermoelastic equation of state of boron subphosphide B₁₂P₂ |
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thermoelastic equation of state of boron subphosphide b₁₂p₂ |
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Solozhenko, V.L. Cherednichenko, K.A. Kurakevych, O.O. |
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Solozhenko, V.L. Cherednichenko, K.A. Kurakevych, O.O. |
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Інститут надтвердих матеріалів ім. В.М. Бакуля НАН України |
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Compressibility of boron subphosphide B₁₂P₂ has been studied under quasi-hydrostatic conditions up to 26 GPa and 2600 K using laser-heated diamond anvil cell and angle-dispersive synchrotron X-ray diffraction.
Вивчено стисливість субфосфіда бору B₁₂P₂ в квазігідростатичних умовах до 26 ГПа і 2600 К в алмазних ковадлах з лазерним нагрівом методом дифракції синхротронного випромінювання.
Изучена сжимаемость субфосфида бора B₁₂P₂ в квазигидростатических условиях до 26 ГПа и 2600 К в алмазных наковальнях с лазерным нагревом методом дифракции синхротронного излучения.
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0203-3119 |
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https://nasplib.isofts.kiev.ua/handle/123456789/160100 |
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Thermoelastic equation of state of boron subphosphide B₁₂P₂ / V.L. Solozhenko, K.A. Cherednichenko, O.O. Kurakevych // Сверхтвердые материалы. — 2017. — № 1. — С. 94-98. — Бібліогр.: 23 назв. — англ. |
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2025-11-25T21:29:27Z |
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www.ism.kiev.ua/stm 94
UDC 661.657/.636:539.58
V. L. Solozhenko1, *, K. A. Cherednichenko1,
O. O. Kurakevych2
1LSPM–CNRS, Université Paris Nord, Villetaneuse, France
2IMPMC, UPMC Sorbonne Universités, Paris, France
*vladimir.solozhenko@univ-paris13.fr
Thermoelastic equation of state of boron
subphosphide B12P2
Compressibility of boron subphosphide B12P2 has been studied under
quasi-hydrostatic conditions up to 26 GPa and 2600 K using laser-heated diamond
anvil cell and angle-dispersive synchrotron X-ray diffraction. 300-K data fit yields the
values of bulk modulus B0 = 192(11) GPa and its first pressure derivative 0B′ = 5.5(12).
It has been found that at ambient pressure the thermal expansion is quasi-linear up to
1300 K with average volume expansion coefficient α = 17.4(1)⋅10–6 K–1. The whole set of
experimental p–V–T data is well described by the Anderson-Grüneisen model with
δT = 6.
Keywords: boron subphosphide, high pressure, equation of state,
thermal expansion.
Boron subphosphide B12P2 is a hard (Vickers hardness
HV = 35(3) GPa [1]) and refractory (melting temperature Tm = 2393(30) K [2] with
positive pressure slope [3]) compound with a wide band gap (~ 2 eV [4]) and supe-
rior chemical resistance. It crystallizes in the R-3m space group [5], similar to α-
rhombohedral boron allotrope (α-B12) stable at high pressures [6], and other
(super)hard boron-rich solids (B6O, B13N2, B4C, etc. [7–10]). Here we report the
p–V–T equation of state (EOS) of boron subphosphide up to 26 GPa and 2600 K.
Polycrystalline powders of single-phase stoichiometric boron subphosphide
were produced by self-propagating high-temperature synthesis [1] and
mechanochemical synthesis [11]. The lattice parameters of synthesized B12P2
(a = 5.992(4), c = 11.861(8) Å) are in a good agreement with the literature data
(a = 5.9879, c = 11.8479 Å [5]).
At pressures 3.9–5.5 GPa and temperatures to 2000 K B12P2 was studied by en-
ergy-dispersive synchrotron X-ray diffraction using MAX80 multianvil system at
F2.1 beamline, DORIS III (DESY). Standard assemblies with hBN pressure
medium were used. The experimental details are described elsewhere [12]. The
sample pressure at different temperatures was determined from the thermal
equation of state of hBN [13]; temperature was measured by a Pt-30%Rh/Pt-6%Rh
thermocouple.
In-situ experiments in the 14–26 GPa pressure range have been performed in a
membrane diamond anvil cell (DAC) using angle-dispersive synchrotron X-ray
diffraction at P02.2 beamline, PETRA III (DESY). We used rhenium gasket and
KCl pressure medium insuring quasi-hydrostatic conditions at high temperatures,
with advantage of chemical inertness with regard to the sample. The
monochromatic X-ray beam (42 keV, λ = 0.2898 Å) was focused down to 2×4 µm.
© V. L. SOLOZHENKO, K. A. CHEREDNICHENKO, O. O. KURAKEVYCH, 2017
ISSN 0203-3119. Сверхтвердые материалы, 2017, № 1 95
The diffraction patterns were recorded using XRD1621 (Perkin-Elmer) flat panel
detector; sample-detector distance was calibrated using CeO2 NIST standard. A
typical acquisition time was 30 seconds. The sample pressure has been determined
using equation of state of KCl [14].
The 300-K p–V data (Fig. 1, a) have been fitted to Murnaghan EOS [15], i.e.,
[ ] 0/1
00 /1)300,0()300,( BBpBVpV ′−′+= , (1)
that allowed us to determine the isothermal bulk modulus B0 = 192(11) and its first
pressure derivative 0B′ = 5.5(12).
Laser heating in a DAC was performed using double-sided off-axis infrared
laser system (continuous fiber YAG laser focused down to 20 µm, λ = 1070 nm).
Temperature measurements were performed through standard grey body radiation
measurement via an Acton spectrometer SP-2356 (Princeton Instruments). The
temperature uncertainties in the 1500–2500 K range were ±40 K.
High-temperature (300–1300 K) thermal expansion of B12P2 in argon at
ambient pressure was studied at MCX beamline of Elettra synchrotron (Trieste).
Debye-Scherrer geometry with rotating quartz-glass capillary was used. X-ray
diffraction patterns were collected in the 5–120 2θ-range (λ = 1.0352 Å) for 120 s
using a translating image plate detector upon stepwise heating with 25-K steps.
Thermal expansion data (Fig. 1, b) shows quasi-linear behavior following the
equation V(T)/V0 = 1 + α(T – 300), where α = 17.4(1)·10–6 K–1, with a 10 % higher
thermal expansivity in the c-axis direction.
0 5 10 15 20 25
0.90
0.92
0.94
0.96
0.98
1.00
R
el
at
iv
e
vo
lu
m
e,
V
/V
0
p, GPa
a
500 1000 1500 2000
335
340
345
350
355
360
365
370
375
380
U
n
it
�c
el
l v
ol
um
e,
Å
3
T, K
1
2
3
4
b
Fig. 1. (a) 300-K equation of state of B12P2: the curve shows the data fit to Murnaghan EOS
(Eq. 1); (b) isobars V(T) at 0.1 MPa (1), 5 (2), 18 (3) and 22 (4) GPa: the curves show the data fit
to the simplified Anderson-Grüneisen model (Eq. 2) with δT = 6.
Temperature dependences of the unit-cell volume (V0 = V(0, 300) = 366.59 Å3
corresponds to 300 K and ambient pressure) at different pressures are shown in
Fig. 1, b. Below 2500 K these dependences are very close to linear ones. The
slopes, however, noticeably depend on pressure. To describe this dependence, we
have used the thermoelastic EOS based on simplified Anderson-Grüneisen model
[16] in the form
[ ] TTTT VpVTVTpV
δ−δ−δ−δ− −+=
/1
)300,0()300,(),0(),( . (2)
www.ism.kiev.ua/stm 96
The fitted value of the Anderson-Grüneisen parameter δT = 6 allows describing
all present experimental p–V–T data for B12P2.
Figure 2 shows the comparison of bulk moduli of boron-rich compounds with
structure related to α-rhombohedral boron. To get the correct scaling, the reported
experimental data for B6O [16, 17], B13N2 [18, 19], B4C [20], and B12As2 [21] were
fitted to Murnaghan EOS. In the case of B12As2 [21], we used the p–V data up to
10 GPa only, i.e., in the range where the pressure medium used (ethanol-metanol)
remains liquid, and conditions are hydrostatic. The general tendency is the decrease
of bulk modulus with increase of covalent radius of an interstitial atom in the
intericosahedral voids. Only boron suboxide does not follow this tendency, most
probably due to the absence of boron atoms connecting oxygen atoms, i.e., O– –O,
contrary to the N–B–N and C–B–C chains in boron subnitride and carbide,
respectively. Ab initio calculations [22, 23] confirm the maximal bulk modulus for
boron subnitride B13N2, although give overestimated B0 values.
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
170
180
190
200
210
220
230
240
P As
experiment, 300 K
CNO
B
ul
k
m
od
ul
us
, G
P
a
Covalent radius, Å
ab initio, 0 K
Fig. 2. Bulk moduli of boron-rich solids with structures related to α-rhombohedral boron as a
function of the covalent radius of an interstitial atom; large circle shows the result of the present
paper.
ACKNOWLEDGEMENTS
The authors thank Dr. V. A. Mukhanov for the samples synthesis, Dr. Y. Le
Godec for the DACs preparation, and Dr. Z. Konôpková (DESY) and Dr. L. Gigli
(Elettra) for assistance in the synchrotron experiments. High-pressure experiments
at DESY have been carried out during beam time allocated to the Projects DESY-
D-I-20090172 EC and DESY-D-I-20120021 EC and received funding from the
European Community's Seventh Framework Programme (FP7/2007-2013) under
grant agreement No 226716. Experiments at Elettra have been performed during
beam time allocated for the Proposal No 20160086. This work was financially
supported by the Agence Nationale de la Recherche (grant ANR-2011-BS08-018)
and European Union’s Horizon 2020 Research and Innovation Programme under
Flintstone2020 project (grant agreement No 689279).
Вивчено стисливість субфосфіда бору B12P2 в квазігідростатичних
умовах до 26 ГПа і 2600 К в алмазних ковадлах з лазерним нагрівом методом дифракції
синхротронного випромінювання. Оцінка даних, отриманих при 300 К, дає значення моду-
ля об’ємного стиснення B0 = 192(11) ГПа і його першої похідної по тиску 0B′ = 5,5(12).
ISSN 0203-3119. Сверхтвердые материалы, 2017, № 1 97
При атмосферному тиску термічне розширення є квазілінійним до 1300 К із середнім
коефіцієнтом об’ємного розширення α = 17,4(1)·10–6 K–1. Всі експериментальні p–V–T
дані добре описуються моделлю Андерсена-Грюназена з δT = 6.
Ключові слова: субфосфід бору, високий тиск, рівняння стану,
термічне розширення.
Изучена сжимаемость субфосфида бора B12P2 в квазигидростатиче-
ских условиях до 26 ГПа и 2600 К в алмазных наковальнях с лазерным нагревом методом
дифракции синхротронного излучения. Оценка данных, полученных при 300 К, дает значе-
ния модуля объемного сжатия B0 = 192(11) ГПа и его первой производной по давлению
0B′ = 5.5(12). При атмосферном давлении термическое расширение является квазилиней-
ным до 1300 К со средним коэффициентом объемного расширения α = 17,4(1)·10–6 K–1.
Все экспериментальные p–V–T данные хорошо описываются моделью Андерсена-
Грюназена с δT = 6.
Ключевые слова: субфосфид бора, высокое давление, уравнение со-
стояния, термическое расширение.
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Received 12.12.16
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>>
/GrayImageDict <<
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>>
/JPEG2000GrayACSImageDict <<
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>>
/JPEG2000GrayImageDict <<
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>>
/AntiAliasMonoImages false
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/MonoImageDict <<
/K -1
>>
/AllowPSXObjects false
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/None
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/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken voor kwaliteitsafdrukken op desktopprinters en proofers. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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/ENU (Use these settings to create Adobe PDF documents for quality printing on desktop printers and proofers. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
/RUS ()
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /NoConversion
/DestinationProfileName ()
/DestinationProfileSelector /NA
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure true
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /NA
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|