### Abstract

A problem in the characterisation of surfaces by means of one- dimensional profile data is the fact that a biased impression is thereby obtained of the summit heights and slopes on the two-dimensional surface. Both are understated in profiles. Recent theoretical developments permit the deduction of two-dimensional surface characteristics from profile measurements of r.m.s. height and r.m.s. slope, the latter being taken in at least three known directions. It is thus possible, using such a group of r.m.s. slope measurements, to characterise the degree of anisotropy of a surface by finding the pair of orthogonal directions along with the r.m.s. profile slope is maximum and minimum and the value of these extreme r.m.s. slopes. This paper consists of (1) a review of the theory of one- dimensional and two-dimensional processes and the relation between the r.m.s. profile slope and the second order moments of a bivariate spectrum, (2) a description of various methods for estimating the r.m.s. slope and their bias and (3) the use of least squares to estimate second order bivariate moments from multiple profile determinations and the relation between these moments for an isotropic surface. (A)

Original language | English (US) |
---|---|

Pages (from-to) | 19-31 |

Number of pages | 13 |

Journal | Wear |

Volume | 49 |

Issue number | 1 , Jul.1978 |

State | Published - Jan 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Surfaces and Interfaces
- Surfaces, Coatings and Films
- Materials Chemistry

### Cite this

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*Wear*, vol. 49, no. 1 , Jul.1978, pp. 19-31.

**Characterization of surface anisotropy.** / McCool, J. I.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Characterization of surface anisotropy.

AU - McCool, J. I.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - A problem in the characterisation of surfaces by means of one- dimensional profile data is the fact that a biased impression is thereby obtained of the summit heights and slopes on the two-dimensional surface. Both are understated in profiles. Recent theoretical developments permit the deduction of two-dimensional surface characteristics from profile measurements of r.m.s. height and r.m.s. slope, the latter being taken in at least three known directions. It is thus possible, using such a group of r.m.s. slope measurements, to characterise the degree of anisotropy of a surface by finding the pair of orthogonal directions along with the r.m.s. profile slope is maximum and minimum and the value of these extreme r.m.s. slopes. This paper consists of (1) a review of the theory of one- dimensional and two-dimensional processes and the relation between the r.m.s. profile slope and the second order moments of a bivariate spectrum, (2) a description of various methods for estimating the r.m.s. slope and their bias and (3) the use of least squares to estimate second order bivariate moments from multiple profile determinations and the relation between these moments for an isotropic surface. (A)

AB - A problem in the characterisation of surfaces by means of one- dimensional profile data is the fact that a biased impression is thereby obtained of the summit heights and slopes on the two-dimensional surface. Both are understated in profiles. Recent theoretical developments permit the deduction of two-dimensional surface characteristics from profile measurements of r.m.s. height and r.m.s. slope, the latter being taken in at least three known directions. It is thus possible, using such a group of r.m.s. slope measurements, to characterise the degree of anisotropy of a surface by finding the pair of orthogonal directions along with the r.m.s. profile slope is maximum and minimum and the value of these extreme r.m.s. slopes. This paper consists of (1) a review of the theory of one- dimensional and two-dimensional processes and the relation between the r.m.s. profile slope and the second order moments of a bivariate spectrum, (2) a description of various methods for estimating the r.m.s. slope and their bias and (3) the use of least squares to estimate second order bivariate moments from multiple profile determinations and the relation between these moments for an isotropic surface. (A)

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UR - http://www.scopus.com/inward/citedby.url?scp=0013710556&partnerID=8YFLogxK

M3 - Article

VL - 49

SP - 19

EP - 31

JO - Wear

JF - Wear

SN - 0043-1648

IS - 1 , Jul.1978

ER -