Crystal truncation rods from miscut surfaces

Petach, Trevor A.; Mehta, Apurva; Toney, Michael F.; Goldhaber-Gordon, David

doi:10.1103/PhysRevB.95.184104

Title: Crystal truncation rods from miscut surfaces

Abstract

Crystal truncation rods are used to study surface and interface structure. Since real surfaces are always somewhat miscut from a low index plane, it is important to study the effect of miscuts on crystal truncation rods. We develop a model that describes the truncation rod scattering from miscut surfaces that have steps and terraces. We show that nonuniform terrace widths and jagged step edges are both forms of roughness that decrease the intensity of the rods. Nonuniform terrace widths also result in a broad peak that overlaps the rods. We use our model to characterize the terrace width distribution and step edge jaggedness on three SrTiO₃ (001) samples, showing excellent agreement between the model and the data, confirmed by atomic force micrographs of the surface morphology. As a result, we expect our description of terrace roughness will apply to many surfaces, even those without obvious terracing.

Authors:

Petach, Trevor A. ^[1]; Mehta, Apurva ^[2]; Toney, Michael F. ^[2]; Goldhaber-Gordon, David ^[1]

Stanford Univ., Palo Alto, CA (United States); The Stanford Institute for Materials and Energy Sciences (SIMES), SLAC National Accelerator Lab., and Stanford Univ., Menlo Park, CA (United States)
SLAC National Accelerator Lab., Menlo Park, CA (United States)

Publication Date:: Mon May 08 00:00:00 EDT 2017

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1368755

Alternate Identifier(s):: OSTI ID: 1355956

Grant/Contract Number:: AC02-76SF00515; ECCS-1542152

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 95; Journal Issue: 18; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE

Citation Formats


                    Petach, Trevor A., Mehta, Apurva, Toney, Michael F., and Goldhaber-Gordon, David. Crystal truncation rods from miscut surfaces.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevB.95.184104.

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                    Petach, Trevor A., Mehta, Apurva, Toney, Michael F., & Goldhaber-Gordon, David. Crystal truncation rods from miscut surfaces.  United States.  https://doi.org/10.1103/PhysRevB.95.184104

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                    Petach, Trevor A., Mehta, Apurva, Toney, Michael F., and Goldhaber-Gordon, David. Mon .  
"Crystal truncation rods from miscut surfaces".  United States.  https://doi.org/10.1103/PhysRevB.95.184104.  https://www.osti.gov/servlets/purl/1368755.

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@article{osti_1368755,

  title        = {Crystal truncation rods from miscut surfaces},

  author       = {Petach, Trevor A. and Mehta, Apurva and Toney, Michael F. and Goldhaber-Gordon, David},

  abstractNote = {Crystal truncation rods are used to study surface and interface structure. Since real surfaces are always somewhat miscut from a low index plane, it is important to study the effect of miscuts on crystal truncation rods. We develop a model that describes the truncation rod scattering from miscut surfaces that have steps and terraces. We show that nonuniform terrace widths and jagged step edges are both forms of roughness that decrease the intensity of the rods. Nonuniform terrace widths also result in a broad peak that overlaps the rods. We use our model to characterize the terrace width distribution and step edge jaggedness on three SrTiO3 (001) samples, showing excellent agreement between the model and the data, confirmed by atomic force micrographs of the surface morphology. As a result, we expect our description of terrace roughness will apply to many surfaces, even those without obvious terracing.},

  doi          = {10.1103/PhysRevB.95.184104},

  journal      = {Physical Review B},

  number       = 18,

  volume       = 95,

  place        = {United States},

  year         = {Mon May 08 00:00:00 EDT 2017},

  month        = {Mon May 08 00:00:00 EDT 2017}

}

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Works referenced in this record:

Surface structure of coherently strained ceria ultrathin films
journal, November 2016

Shi, Yezhou; Stone, Kevin H.; Guan, Zixuan
Physical Review B, Vol. 94, Issue 20
DOI: 10.1103/PhysRevB.94.205420

Integrated Intensities Using a Six-Circle Surface X-ray Diffractometer
journal, October 1997

Vlieg, E.
Journal of Applied Crystallography, Vol. 30, Issue 5
DOI: 10.1107/S0021889897002537

Structural Basis for the Conducting Interface between ${LaAlO}_{3}$ and ${SrTiO}_{3}$
journal, October 2007

Willmott, P. R.; Pauli, S. A.; Herger, R.
Physical Review Letters, Vol. 99, Issue 15, Article No. 155502
DOI: 10.1103/PhysRevLett.99.155502

Atomic-layer synthesis and imaging uncover broken inversion symmetry in La $_{2 - x}$ Sr $_{x}$ CuO $_{4}$ films
journal, January 2013

Yacoby, Yizhak; Zhou, Hua; Pindak, Ron
Physical Review B, Vol. 87, Issue 1
DOI: 10.1103/PhysRevB.87.014108

X-ray scattering from real surfaces: Discrete and continuous components of roughness
journal, August 2006

Dale, Darren; Fleet, Aaron; Suzuki, Y.
Physical Review B, Vol. 74, Issue 8
DOI: 10.1103/PhysRevB.74.085419

Structure of the Hydrated -Al2O3 (0001) Surface
journal, May 2000

Eng, P. J.
Science, Vol. 288, Issue 5468
DOI: 10.1126/science.288.5468.1029

Misoriented surfaces with randomly distributed steps
journal, June 1984

Presicci, M.; Lu, T. -M.
Surface Science, Vol. 141, Issue 1
DOI: 10.1016/0039-6028(84)90208-5

Crystal truncation rods and surface roughness
journal, March 1986

Robinson, I. K.
Physical Review B, Vol. 33, Issue 6
DOI: 10.1103/PhysRevB.33.3830

Influence of miscut on crystal truncation rod scattering
journal, April 1999

Munkholm, A.; Brennan, S.
Journal of Applied Crystallography, Vol. 32, Issue 2
DOI: 10.1107/S0021889898005159

Diffraction from disordered vicinal surfaces with alternating terraces
journal, June 2007

Wollschläger, Joachim; Tegenkamp, Christoph
Physical Review B, Vol. 75, Issue 24
DOI: 10.1103/PhysRevB.75.245439

Phase separation and step roughening of vicinal Si(111): An x-ray-scattering study
journal, March 1995

Held, G. A.; Goodstein, D. M.; Brock, J. D.
Physical Review B, Vol. 51, Issue 11
DOI: 10.1103/PhysRevB.51.7269

Self-Assembly of n-Alkyl Thiols as Disulfides on Au(111)
journal, November 1994

Fenter, P.; Eberhardt, A.; Eisenberger, P.
Science, Vol. 266, Issue 5188
DOI: 10.1126/science.266.5188.1216

Elements of Modern X-ray Physics
book, March 2011

Als-Nielsen, Jens; McMorrow, Des
DOI: 10.1002/9781119998365

Anisotropic roughening of vicinally miscut Ag(110): X-ray-reflection profile analysis using the domain-matrix method
journal, July 1995

Pflanz, S.; Meyerheim, H. L.; Moritz, W.
Physical Review B, Vol. 52, Issue 4
DOI: 10.1103/PhysRevB.52.2914

Atomic Structure of the Polar NiO(111)- $p (2 \times 2)$ Surface
journal, March 2000

Barbier, A.; Mocuta, C.; Kuhlenbeck, H.
Physical Review Letters, Vol. 84, Issue 13
DOI: 10.1103/PhysRevLett.84.2897

Calculation of x-ray-diffraction profiles from vicinal surfaces
journal, March 1995

Held, G. A.; Brock, J. D.
Physical Review B, Vol. 51, Issue 11
DOI: 10.1103/PhysRevB.51.7262

X-ray Crystal Truncation Rod Studies of Surface Oxidation and Reduction on Pt(111)
journal, March 2016

Liu, Yihua; Barbour, Andi; Komanicky, Vladimir
The Journal of Physical Chemistry C, Vol. 120, Issue 29
DOI: 10.1021/acs.jpcc.6b00492

Diffraction by a surface with terraces distribution: the Phase Matrix Method
journal, July 1998

Croset, B.; de Beauvais, C.
Surface Science, Vol. 409, Issue 3
DOI: 10.1016/S0039-6028(98)00182-4

Surface X-ray diffraction
journal, May 1992

Robinson, I. K.; Tweet, D. J.
Reports on Progress in Physics, Vol. 55, Issue 5
DOI: 10.1088/0034-4885/55/5/002

Scattering of X-rays from crystal surfaces
journal, December 1985

Andrews, S. R.; Cowley, R. A.
Journal of Physics C: Solid State Physics, Vol. 18, Issue 35
DOI: 10.1088/0022-3719/18/35/008

Diffraction from stepped surfaces II. Arbitrary terrace distributions
journal, October 1985

Pukite, P. R.; Lent, C. S.; Cohen, P. I.
Surface Science Letters, Vol. 161, Issue 1
DOI: 10.1016/0167-2584(85)90512-2

Angle calculations for a `4S+2D' six-circle diffractometer
journal, August 1999

You, H.
Journal of Applied Crystallography, Vol. 32, Issue 4
DOI: 10.1107/S0021889899001223

The atomic surface structure of SrTiO3(001) in air studied with synchrotron X-rays
journal, December 2005

Vonk, V.; Konings, S.; van Hummel, G. J.
Surface Science, Vol. 595, Issue 1-3
DOI: 10.1016/j.susc.2005.08.010

Voltage-dependent ordering of water molecules at an electrode–electrolyte interface
journal, March 1994

Toney, Michael F.; Howard, Jason N.; Richer, Jocelyn
Nature, Vol. 368, Issue 6470
DOI: 10.1038/368444a0

Oxygen chemisorption on Cu(110): A structural determination by x-ray diffraction
journal, March 1990

Feidenhans’l, R.; Grey, F.; Johnson, R. L.
Physical Review B, Vol. 41, Issue 8
DOI: 10.1103/PhysRevB.41.5420

Diffraction from surfaces with randomly distributed steps
journal, August 1982

Lu, T. -M.; Lagally, M. G.
Surface Science, Vol. 120, Issue 1
DOI: 10.1016/0039-6028(82)90274-6

Angle calculations for 3- and 4-circle X-ray and neutron diffractometers
journal, April 1967

Busing, W. R.; Levy, H. A.
Acta Crystallographica, Vol. 22, Issue 4
DOI: 10.1107/S0365110X67000970

Atomic Control of the SrTiO₃ Crystal Surface
journal, December 1994

Kawasaki, M.; Takahashi, K.; Maeda, T.
Science, Vol. 266, Issue 5190, p. 1540-1542
DOI: 10.1126/science.266.5190.1540

Works referencing / citing this record:

How heteroepitaxy occurs on strontium titanate
journal, April 2019

Cook, Seyoung; Letchworth-Weaver, Kendra; Tung, I-Cheng
Science Advances, Vol. 5, Issue 4
DOI: 10.1126/sciadv.aav0764

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Similar Records

Title: Crystal truncation rods from miscut surfaces

Abstract

Citation Formats

Surface structure of coherently strained ceria ultrathin films journal, November 2016

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Structural Basis for the Conducting Interface between LaAlO3 and SrTiO3 journal, October 2007

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Influence of miscut on crystal truncation rod scattering journal, April 1999

Diffraction from disordered vicinal surfaces with alternating terraces journal, June 2007

Phase separation and step roughening of vicinal Si(111): An x-ray-scattering study journal, March 1995

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Diffraction from stepped surfaces II. Arbitrary terrace distributions journal, October 1985

Angle calculations for a `4S+2D' six-circle diffractometer journal, August 1999

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Voltage-dependent ordering of water molecules at an electrode–electrolyte interface journal, March 1994

Oxygen chemisorption on Cu(110): A structural determination by x-ray diffraction journal, March 1990

Diffraction from surfaces with randomly distributed steps journal, August 1982

Angle calculations for 3- and 4-circle X-ray and neutron diffractometers journal, April 1967

Atomic Control of the SrTiO3 Crystal Surface journal, December 1994

How heteroepitaxy occurs on strontium titanate journal, April 2019

Surface structure of coherently strained ceria ultrathin films
journal, November 2016

Integrated Intensities Using a Six-Circle Surface X-ray Diffractometer
journal, October 1997

Structural Basis for the Conducting Interface between ${LaAlO}_{3}$ and ${SrTiO}_{3}$
journal, October 2007

Atomic-layer synthesis and imaging uncover broken inversion symmetry in La $_{2 - x}$ Sr $_{x}$ CuO $_{4}$ films
journal, January 2013

X-ray scattering from real surfaces: Discrete and continuous components of roughness
journal, August 2006

Structure of the Hydrated -Al2O3 (0001) Surface
journal, May 2000

Misoriented surfaces with randomly distributed steps
journal, June 1984

Crystal truncation rods and surface roughness
journal, March 1986

Influence of miscut on crystal truncation rod scattering
journal, April 1999

Diffraction from disordered vicinal surfaces with alternating terraces
journal, June 2007

Phase separation and step roughening of vicinal Si(111): An x-ray-scattering study
journal, March 1995

Self-Assembly of n-Alkyl Thiols as Disulfides on Au(111)
journal, November 1994

Elements of Modern X-ray Physics
book, March 2011

Anisotropic roughening of vicinally miscut Ag(110): X-ray-reflection profile analysis using the domain-matrix method
journal, July 1995

Atomic Structure of the Polar NiO(111)- $p (2 \times 2)$ Surface
journal, March 2000

Calculation of x-ray-diffraction profiles from vicinal surfaces
journal, March 1995

X-ray Crystal Truncation Rod Studies of Surface Oxidation and Reduction on Pt(111)
journal, March 2016

Diffraction by a surface with terraces distribution: the Phase Matrix Method
journal, July 1998

Surface X-ray diffraction
journal, May 1992

Scattering of X-rays from crystal surfaces
journal, December 1985

Diffraction from stepped surfaces II. Arbitrary terrace distributions
journal, October 1985

Angle calculations for a `4S+2D' six-circle diffractometer
journal, August 1999

The atomic surface structure of SrTiO3(001) in air studied with synchrotron X-rays
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Voltage-dependent ordering of water molecules at an electrode–electrolyte interface
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Oxygen chemisorption on Cu(110): A structural determination by x-ray diffraction
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Diffraction from surfaces with randomly distributed steps
journal, August 1982

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Atomic Control of the SrTiO₃ Crystal Surface
journal, December 1994

How heteroepitaxy occurs on strontium titanate
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